During his 2007 trial, Derrick Cartwright asserted an alibi defense to charges of murder and other crimes in connection with the shooting death of Kevin Stafford. Cartwright was convicted and sentenced to serve life in prison plus five years. On direct appeal, he claimed among other things that his trial counsel provided ineffective assistance by failing to challenge Detective Andrew Tyner's testimony that Cartwright had not mentioned his alibi during his post-arrest police interview. Cartwright contended that during a preliminary hearing, Detective Bernard Spicer, the lead investigator in the case, testified that Detective Tyner told him that Cartwright had mentioned his alibi during the interview. This Court affirmed Cartwright's convictions, rejecting his claim that his trial counsel provided ineffective assistance by failing to introduce Detective Spicer's testimony; we held that Cartwright had not shown prejudice because at the motion for new trial hearing, he failed to call Detective Spicer as a witness or introduce a transcript of the detective's preliminary hearing testimony. See Cartwright v. State, 291 Ga 498, 500, 731 S.E.2d 353 (2012).
Cartwright then filed a petition for habeas corpus, alleging among other things that his appellate counsel provided ineffective assistance by failing to introduce evidence to prove trial counsel's ineffectiveness in failing to impeach Detective Tyner. The habeas court denied the petition. We granted Cartwright's application to appeal to consider whether the habeas court erred in ruling that Cartwright had not shown that his appellate counsel provided ineffective assistance. We conclude that the habeas court's ruling was erroneous, and we therefore reverse the denial of habeas relief.
1. (a) The evidence presented at Cartwright's trial showed the following.1 In the *171early morning hours of April 3, 2006, police officers responded to reports of a car crash at the corner of 35th Street and 6th Avenue in Columbus. At the scene, officers found a car that had crashed into some steps outside a house; in the driver's seat was Kevin Stafford, who had been shot once in the neck. He was taken to a hospital, where he soon died from the gunshot wound.
Officers investigating the shooting found a shell casing, a bullet jacket, and a bullet fragment in Stafford's car. A ballistics examiner later determined that the bullet jacket and fragment were fired from a .380-caliber pistol and that the shell casing was consistent with being fired from a .380-caliber pistol. The police did not find a gun at the scene.
About two weeks later, an officer interviewed Diane Ruhl, who lived on 6th Avenue. She said that she had seen Derrick Cartwright shoot Stafford after Cartwright asked Stafford, "where is my $40.00, mother f* *ker?" Ruhl also identified Cartwright as the shooter in a photo lineup. The police then obtained a warrant for Cartwright's arrest, and he turned himself in on April 26. He was interviewed by Detective Andrew Tyner later that day. On November 28, 2006, a Muscogee County grand jury indicted Cartwright for malice murder, felony murder based on aggravated assault, aggravated assault, and possession of a firearm during the commission of a crime.
At a trial that began on April 30 and ended on May 3, 2007, the State presented testimony from four eyewitnesses who identified Cartwright in court as the shooter. Ruhl and her friend Antonio Willis, who is known as "T-Mac" and who was selling cocaine near 35th Street at the time of the shooting, both testified that sometime between 3:00 a.m. and 4:30 a.m., Stafford pulled his car over on 6th Avenue, and Cartwright approached Stafford, who was sitting in the driver's seat; Cartwright told Stafford that he owed Cartwright $40, and they began to argue; Cartwright shot Stafford; and Stafford then fled in his car before crashing. Willis testified that Cartwright had been carrying a .380-caliber gun earlier that evening.2 Willis also testified that on the day after the murder, Cartwright asked him if anyone had said that Cartwright was involved in the shooting. Willis was asked at trial if he had any involvement in the shooting, and he denied it.
In addition, Marcus Brown and his sister, who had both been at a party near 6th Avenue just before the murder, identified Cartwright as the shooter in photo lineups before trial and later testified that they saw Cartwright shoot Stafford.3 Brown also testified that while he was in a holding cell in the courthouse with Cartwright on the second day of the trial, Cartwright had threatened him, saying that he "had better tell people [he] didn't know [Cartwright]."
Cartwright presented an alibi defense at trial. He did not testify, but he presented testimony from five witnesses-his mother, two sisters, his sister's boyfriend, and a family *172friend-to support his claim.4 The defense also presented testimony from two other witnesses who claimed that Willis told them that he shot Stafford over a drug dispute.5 In addition, Cartwright impeached Ruhl and Willis with evidence of their felony drug convictions, elicited Ruhl's admission that she had used cocaine just before the shooting, argued in closing that Brown and his sister were biased in favor of the State because Brown was facing felony charges at the time of trial, and pointed out inconsistencies between the witnesses' accounts of the shooting.6
To rebut Cartwright's alibi defense, the prosecutor asked Detective Tyner multiple questions to establish that Cartwright had not mentioned his alibi during his post-arrest interview.7 Cartwright's trial counsel did not *173cross-examine Detective Tyner about Cartwright's statements during the interview.8 During closing arguments, the prosecutor repeatedly asserted that Cartwright never mentioned his alibi to Detective Tyner; said that Detective Tyner's testimony in that respect was "undisputed evidence"; and argued over and over again that Cartwright must have invented his alibi after his interview and then asked his mother and sister to testify to the alibi at his preliminary hearing a week later.9
The jury found Cartwright not guilty of malice murder but guilty of felony murder, aggravated assault, and possession of a firearm during the commission of a crime.10 He was sentenced to serve life in prison for felony murder and five consecutive years for the firearm offense; the aggravated assault count merged.
(b) Cartwright filed a motion for new trial, which he amended twice with new counsel, claiming among other things that his trial counsel provided ineffective assistance by failing to impeach Detective Tyner's testimony that Cartwright had not mentioned his alibi during his post-arrest interview. Cartwright *174asserted that at his May 2006 preliminary hearing, Detective Bernard Spicer, the lead investigator in the case, testified that Detective Tyner told him that Cartwright said in his interview that he was at home with his mother and sister at the time of the murder. After an evidentiary hearing, the trial court denied Cartwright's motion for new trial in November 2011.
Cartwright then filed an appeal raising the same ineffectiveness claim, among other things.11 In September 2012, this Court affirmed Cartwright's convictions. See Cartwright, 291 Ga. at 501, 731 S.E.2d 353. As to his claim that his trial counsel provided ineffective assistance by failing to impeach Detective Tyner's testimony, we noted that a defendant who bases an ineffective assistance claim on counsel's decision not to call a particular witness may not rely on hearsay or speculation regarding what the witness would have testified to. See id. at 500, 731 S.E.2d 353. We then said:
Cartwright did not call Detective Spicer to testify at the motion for new trial hearing, nor did he introduce a transcript of the detective's testimony from the preliminary hearing. As such, Cartwright has failed to establish a reasonable probability that the outcome of the trial would have been different if Detective Spicer's testimony had been introduced to impeach that of Detective Tyner. Therefore, the second prong of the Strickland test is not met.
Id. (referring to Strickland v. Washington, 466 U.S. 668, 687, (104 S.Ct. 2052, 80 L.Ed.2d 674) (1984) ).
(c) In September 2016, Cartwright, through new counsel, filed a petition for habeas corpus raising two claims, only one of which is raised in this appeal: that his appellate counsel provided ineffective assistance by failing to introduce evidence at the motion for new trial hearing to prove trial counsel's ineffectiveness in failing to impeach Detective Tyner's testimony that Cartwright had not mentioned his alibi during his post-arrest interview. At an evidentiary hearing in January 2017, Cartwright introduced into evidence, without objection, the transcript of his preliminary hearing. The transcript shows that Cartwright's pre-trial attorney asked Detective Spicer: "Do you know if ... within [Cartwright's post-arrest interview, Cartwright] told Detective Tyner that ... at the time of this alleged murder ... he was at home with his mama and his sister?" Detective Spicer answered, "Yes, sir. Detective Tyner did relate that to me."
At the habeas hearing, Cartwright also introduced into evidence, without objection, an affidavit from Detective Spicer stating that "Detective Tyner did relate to me that Cartwright stated [in the interview] that at the time of the murder, he was at home with his mother and sister." Detective Spicer also said that Cartwright's trial and appellate attorneys never interviewed him about the case or called him as a witness. See OCGA § 9-14-48 (a) (stating that a habeas court "may receive proof by ... sworn affidavits"). Cartwright did not call his trial counsel to testify at the habeas hearing, and his appellate counsel was deceased by then.
The habeas court denied Cartwright relief. The court pretermitted the question of deficient performance and concluded that Cartwright had not established prejudice on this ineffective assistance claim because he had presented his alibi defense at trial through the testimony of several other witnesses, but the jury had chosen to reject that defense and to credit the testimony of the State's witnesses instead.
Cartwright filed a timely notice of appeal and a timely application for a certificate of probable cause to appeal. We granted his application to address whether Cartwright's appellate counsel provided ineffective assistance by failing to introduce evidence to support Cartwright's claim that his trial counsel was ineffective for failing to impeach Detective Tyner. Because appellate counsel was ineffective, we will reverse the habeas court's judgment.
*1752. To prevail on a claim of ineffective assistance of appellate counsel, a habeas petitioner must show that his appellate counsel performed deficiently and that the deficiency prejudiced his appeal. See Taylor v. Metoyer, 299 Ga. 345, 348, 788 S.E.2d 376 (2016). See also Strickland, 466 U.S. at 687, 104 S.Ct. 2052. To prove deficient performance, the petitioner must show that appellate counsel performed his duties in an objectively unreasonable way, considering all the circumstances and in the light of prevailing professional norms. See Strickland, 466 U.S. at 687-690, 104 S.Ct. 2052. To overcome the strong presumption that counsel performed reasonably, the petitioner must show that " 'no reasonable lawyer would have done what his lawyer did, or would have failed to do what his lawyer did not.' " Brown v. State, 302 Ga. 454, 457, (807 S.E.2d 369) (2017) (citation omitted). See also Taylor, 299 Ga. at 348, 788 S.E.2d 376.
To demonstrate prejudice, the habeas petitioner must show that there is a reasonable probability that, but for appellate counsel's unprofessional errors, the result of the appeal would have been different. See Taylor, 299 Ga. at 348, 788 S.E.2d 376. "A reasonable probability is a probability sufficient to undermine confidence in the outcome." Strickland, 466 U.S. at 694, 104 S.Ct. 2052. To determine prejudice involving a claim that appellate counsel provided ineffective assistance by failing to properly raise or prove a claim of ineffective assistance of trial counsel, the petitioner must demonstrate that the underlying ineffectiveness-of-trial-counsel claim would have had a reasonable probability of success. See Gramiak v. Beasley, 304 Ga. 512, 513, 820 S.E.2d 50 (2018). Accordingly, under these circumstances, the petitioner must show that his trial counsel performed deficiently, and that, but for trial counsel's deficient performance, there is a reasonable probability that the outcome of the trial would have been different. See id.
(a) Turning first to the issue of trial counsel's ineffectiveness, we begin by addressing whether trial counsel performed deficiently by failing to present evidence at trial tracking Detective Spicer's preliminary hearing testimony and habeas hearing affidavit-a question that the habeas court pretermitted. At trial, a major focus of Detective Tyner's testimony was Cartwright's purported failure to mention his alibi during his post-arrest interview. Evidence that Detective Tyner told Detective Spicer that Cartwright did assert his alibi in the interview would have directly contradicted Detective Tyner's testimony-with that evidence coming from a fellow police officer and the lead investigator for Cartwright's case.
Moreover, the evidence from Detective Spicer would have been admissible not only for the limited purpose of impeaching Detective Tyner, see former OCGA § 24-9-83 ("A witness may be impeached by contradictory statements previously made by him as to matters relevant to his testimony and to the case."), but also as substantive evidence that Cartwright provided his alibi during the interview, see Holiday v. State, 272 Ga. 779, 780, 534 S.E.2d 411 (2000) (explaining that "a prior inconsistent statement of a witness who takes the stand and is subject to cross-examination is admissible both to impeach the witness and as substantive evidence").12 In addition, if this evidence contradicting Detective Tyner had been introduced, the prosecutor would have had to omit or at least substantially soften his emphasis in closing argument on Cartwright's supposed post-interview invention of his alibi.
Cartwright's trial counsel, however, did not even cross-examine Detective Tyner about Cartwright's alleged failure to mention his alibi, much less present evidence of Detective Tyner's prior inconsistent statement to Detective Spicer. Trial counsel acknowledged at the motion for new trial hearing that the preliminary hearing transcript was included in discovery, but said that he could not remember why he had not introduced evidence from Detective Spicer; in his habeas affidavit, Detective Spicer noted that he was never interviewed by trial counsel. There is no indication (and the warden does not argue)
*176that Detective Spicer would not have been credible or would have refused to testify if called. See Fisher v. State, 299 Ga. 478, 484, 788 S.E.2d 757 (2016). It appears that trial counsel simply whiffed on this issue. Although the scope of cross-examination will rarely support a claim of deficient performance, no reasonably competent defense attorney would have decided to forgo presenting this evidence to cast doubt on the credibility of the State and one of its key witnesses and to bolster Cartwright's alibi defense. See Taylor, 299 Ga. at 349, 788 S.E.2d 376.
(b) Whether Cartwright has demonstrated a reasonable probability that trial counsel's failure to introduce Detective Spicer's testimony affected the outcome of the trial is a closer question. The habeas court concluded that Cartwright had not shown Strickland prejudice because he had presented his alibi defense at trial through several other witnesses. That reasoning, however, misses the point for which the defense would have offered Detective Spicer's testimony. The detective's testimony would have been relatively insignificant to bolster the credibility of the five witnesses who testified that Cartwright was at his family's apartment on the night of the shooting-but it was critical to rebut the State's vociferous assertion that Cartwright invented that alibi after his post-arrest interview.
The State's claim that Cartwright failed to provide his alibi to Detective Tyner during the post-arrest interview was not a passing comment that the jury might have overlooked; it was instead a targeted attack on the truthfulness of Cartwright's alibi defense-his primary defense at trial. The prosecutor had Detective Tyner testify repeatedly and definitively that Cartwright had not mentioned his alibi in any way during the interview, see footnote 7 above; the prosecutor then relied on that "undisputed evidence" during closing argument to assert repeatedly that Cartwright invented his alibi defense after the interview and then convinced his alibi witnesses to testify on his behalf, see footnote 9 above.
The emphasis that the State placed on its claim that Cartwright belatedly invented his alibi is particularly significant in light of the nature of the evidence against Cartwright. There was no physical evidence linking him to the shooting, and although the State presented four witnesses who said that they saw Cartwright shoot Stafford, the defense substantially impeached each of them. Willis and Ruhl were impeached with their felony drug convictions; two defense witnesses testified that Willis had told them that he shot Stafford; Ruhl admitted that she was close to Willis and that she had used cocaine shortly before the shooting; Brown had felony charges pending against him and waffled in his pretrial accusation against Cartwright, asserting at one point during his police interview that Willis was the shooter; Brown's sister had reason to support his testimony; and each of the witnesses gave a different account of the events surrounding the shooting. Cartwright offered not one or two but five witnesses in support of his alibi. Indeed, during jury deliberations, the trial court noted that the case was "close" and hinged on witness credibility.13
Given the less than overwhelming evidence of Cartwright's guilt, his affirmative defense of alibi supported by multiple witnesses, and the importance of Detective Tyner's testimony to the State's efforts to disprove that defense, we conclude that trial counsel's failure to introduce Detective Spicer's contrary testimony had a reasonable probability of affecting the outcome of the trial. See, e.g., Bryant v. State, 301 Ga. 617, 621-622, 800 S.E.2d 537 (2017) (concluding that the appellant showed Strickland prejudice resulting from trial counsel's failure to move to suppress the only physical evidence connecting *177the appellant to the murder, because the credibility of three eyewitnesses was "substantially challenged," evidence was presented that one of those witnesses was actually the shooter, and the State relied heavily on the illegally obtained evidence in its closing argument); Kennebrew v. State, 299 Ga. 864, 874, 792 S.E.2d 695 (2016) (concluding that the appellant showed Strickland prejudice when the State focused in its closing argument on evidence trial counsel should have had suppressed, and the other evidence was not overwhelming).
(c) Because Cartwright has demonstrated that his trial counsel provided ineffective assistance, any deficiency in appellate counsel's proving that ineffectiveness-of-trial-counsel claim prejudiced his appeal. See Gramiak, 304 Ga. at 513, 820 S.E.2d 50. The only question remaining is whether appellate counsel performed deficiently by failing to introduce evidence of Detective Spicer's testimony at the motion for new trial hearing to support the ineffectiveness-of-trial-counsel claim.
We see no good reason why a competent appellate lawyer would have failed to raise and support that claim under these circumstances; indeed, Cartwright's appellate counsel did raise the claim (along with only two other claims, which were easily rejected). As we held in Cartwright, however, appellate counsel failed to introduce evidence to support the claim at the motion for new trial hearing. No reasonable attorney would have failed to present the readily available evidence from Detective Spicer, which was essential to proving trial counsel's ineffectiveness.
Counsel from the Attorney General's office, representing the warden here, do not offer any good reason why this claim should not have been raised and supported. Instead, they argue that this Court erred when we held in Cartwright's prior appeal that he could not show the prejudice required to establish that trial counsel was ineffective because appellate counsel "did not call Detective Spicer to testify at the motion for new trial hearing, nor did he introduce a transcript of the detective's testimony from the preliminary hearing." Cartwright, 291 Ga. at 500, 731 S.E.2d 353. The Attorney General's office now argues that review of the motion for new trial hearing transcript reveals that appellate counsel did introduce some evidence to support the ineffectiveness-of-trial-counsel claim and, therefore, appellate counsel did not perform deficiently.14
That argument, however, ignores the law-of-the-case doctrine. Under that doctrine, "any ruling by the Supreme Court or the Court of Appeals in a case shall be binding in all subsequent proceedings in that case in the lower court and in the Supreme Court or the Court of Appeals." OCGA § 9-11-60 (h). "It is well-established that the law of the case doctrine applies to holdings by appellate courts in criminal cases," see Hollmon v. State, Case No. S18A1464, --- Ga. ----, ----, 823 S.E.2d 771, 2019 WL 417911, at *1 (decided Feb. 4, 2019), including in habeas corpus proceedings following a direct appeal, see Roulain v. Martin, 266 Ga. 353, 354, 466 S.E.2d 837 (1996). Accordingly, our previous conclusion that Cartwright's appellate counsel failed to call Detective Spicer to testify at the motion for new trial hearing or introduce a transcript of the detective's testimony from the preliminary hearing was binding on the habeas court and binds this Court as well, regardless of whether that conclusion was correct. See id. See also Buckner v. Barrow, 297 Ga. 68, 69, 772 S.E.2d 703 (2015).
We therefore conclude that appellate counsel provided ineffective assistance, and the habeas court's ruling to the contrary was erroneous. Accordingly, we reverse the habeas *178court's denial of Cartwright's petition for a writ of habeas corpus.
Judgment reversed.
All the Justices concur.