Defendant was indicted for arson but was prosecuted for, and convicted of, burning an uninhabited house in violation of N.C. Gen. Stat. § 14-62 (1993). He was also convicted of first-degree murder.
The State’s evidence, except where otherwise noted, showed the following. In February 1996, defendant and his wife, Willena, were living in Clarkton. They had separate jobs. Willena worked from 7:00 a.m. to 3:30 p.m., and defendant worked from 11:00 p.m. to 7:30 a.m. The couple was having marital problems which dated to at least 1996. In October 1995, Willena had told defendant she thought they needed to separate, but they did not.
On 18 February 1996, a Sunday, Willena placed a telephone call from her home to the Nakima home of her mother, Florence, and her stepfather, Henry Waymon Gore. Waymon was in the process of remodeling a mobile home just over two miles from where Willena and defendant lived. Willena asked if she could rent the mobile home once it was finished, and Waymon agreed.
Willena did not tell defendant that she planned to move out. Just a day or two later, however, defendant asked her whether she thought she was going to like her new home. Willena was surprised by defendant’s remark. When she was interviewed by an SBI agent later that week, Willena stated that defendant had told her that if anyone tried to interfere with their marriage, “[t]hey would pay.”
On Wednesday, 21 February 1996, around 11:30 p.m., Willena called Waymon and again asked him about the mobile home. Waymon said he would have it ready for her by the first of the month. During the telephone conversation, Florence told Willena that both she and her husband would be working at the mobile home the next day.
When defendant went to work that night, he was dressed, as was his custom, in blue jeans, a blue Wrangler shirt, a camouflage jacket, and a black baseball cap. He had no fresh scratches on his neck when he went to work.
*175Willena went to work before 7:00 a.m. on Thursday, 22 February 1996, the day of the murder. Waymon drove from his house to the mobile home around the same time.
Defendant got off work at 7:30 a.m. A little before 9:00 a.m., defendant testified, he stopped by the mobile home where Waymon was working and talked with him a few minutes about a hunting trip. Florence was not there. Defendant later told investigators he had not stopped by the mobile home and spoken to Waymon that day; when he testified at trial, he said that he lied during the previous conversation.
Florence left for the mobile home between 8:00 and 8:30 a.m. and arrived there between 9:00 and 9:30 a.m, parking the car at the end of the mobile home closest to the street. She went in and helped Waymon with some work. She eventually returned to the car to take a break. She sat in the passenger seat with the door ajar.
About fifteen minutes passed. Florence noticed defendant walking towards the mobile home from a nearby railroad track. He had a gun in his left hand and a plastic jug filled with liquid in his right hand. The gun had a silver barrel with a black stock. Defendant was wearing blue jeans, a “green army jacket,” and a black cap.
Around the same time, a neighbor, Kelly McQuage, was hanging clothes in her yard when she saw a man walk to Waymon’s mobile home from the railroad tracks. The man was wearing “work clothes,” including a blue or dark green shirt and a dark baseball cap. According to McQuage, he was holding a rifle or shotgun in his left hand. When he reached the corner of the mobile home, he bent down and picked something up or put something down. He then walked around the mobile home and out of McQuage’s line of sight.
From the passenger seat, Florence saw defendant pass directly in front of her car and enter the mobile home, carrying the gun and the jug. The two did not make eye contact; the right side of defendant’s body was facing Florence. She saw a scratch, which appeared to be fresh, on the right side of his neck. She was too scared to move until defendant had gone inside the mobile home. She then got out of her car and walked around the end of the trailer to see if she could see anyone. She could not, but she did hear Waymon say, “No, don’t.” There was a loud thud.
Florence ran as fast as she could to a house about 100 to 125 feet away. She burst through the front door and told the people in the *176house, including Virginia Hainsey, who is acquainted with the Britts and the Gores, that defendant had gone into the mobile home with a gun. Hainsey looked out the window and saw a man, whom she is “ninety-nine percent sure” was defendant, walking from the mobile home. He was wearing a camouflage shirt, dark pants, and a dark baseball cap. He was carrying a gun in his right hand. He went back across the railroad tracks, paused, looked back in the direction of the mobile home, turned, and walked through a clearing in the direction of his house. He was carrying a gun with a bright barrel and a darker stock. According to Hainsey, defendant “wasn’t in any hurry.”
Florence and Hainsey ran to the mobile home. It was on fire. Flames shot through the windows, and the front door blew out. No one could get inside.
Later, after the fire had been extinguished, Waymon’s body was found in the mobile home. A claw hammer was on the floor near his feet. An autopsy revealed that Waymon sustained seven blows to the head and that his skull was fractured in three places. Medical expert testimony suggested that these blows could have been struck with the claw hammer. He also sustained five stab wounds to the chest, two of which pierced his heart. Testimony was that these wounds were probably inflicted with a knife. The chest and head wounds, in combination, caused his death.
The fire began, it was determined, when someone poured a liquid accelerant like gasoline onto the floor of the mobile home and across the victim and ignited it. The mobile home and the victim’s body were burned extensively.
Later that day, when the police searched defendant’s house, they found the blue jeans and shirt defendant had worn to work soaking in the washing machine. They also found his black cap and camouflage jacket. They did not find defendant’s work belt, which is where he kept a pocketknife. The door to the gun cabinet was ajar, and a .22 caliber rifle with a silver barrel and black stock was missing from the premises. Willena had just cleaned that gun and closed the gun cabinet door the night before the murder.
Subsequently, Willena discovered a tape recorder, with an apparent phone bugging attachment, in a small hole in the utility room at her house. A tape in the recorder contained several of Willena’s phone conversations, conversations that transpired prior to her discussions with Florence and Waymon about moving into the mobile home. *177Willena was unaware that her conversations had been taped. Defendant testified that he had hooked up the recorder in November 1995 and used it sporadically through January 1996 because he suspected Willena of infidelity.
Defendant’s testimony was that, around 10:00 a.m. the day of the murder, he started driving around looking for the family dog, which had been missing for several weeks. After forty minutes, defendant stated, he returned to his house, lay down on a tanning bed for thirty minutes, and took a shower. According to defendant, he first learned of the murder from his brother, Kenneth, who came to the house and told him he was a suspect. Defendant testified that his relationship with the victim, his stepfather-in-law, had been friendly, although he had not spoken to the victim in the two months preceding his death.
An SBI agent saw defendant around 3:30 p.m. that day. Just as Florence had told him, defendant had a fresh scratch on the right side of his neck. Defendant testified that he had scratched his neck that night at work. He further testified that he had not seen Willena or Florence after receiving the scratch, and he agreed with the prosecutor that, without having seen him, Florence could not have known about the scratch.
[1] We agree with defendant that his conviction for burning an uninhabited house should be vacated. The version of G.S. 14-62 in effect at the time of these events provided in relevant part,
If any person shall wantonly and willfully set fire to or burn or cause to be burned . . . any uninhabited house, . . . whether the same . . . shall then be in the possession of the offender, or in the possession of any other person, he shall be punished as a Class F felon.
N.C. Gen. Stat. § 14-62 (1993). Because defendant was indicted for arson, and not burning an uninhabited house, his conviction of burning an uninhabited house is valid only if that crime is a lesser included offense of arson. N.C. Gen. Stat. § 15-170 (1983); State v. Riera, 276 N.C. 361, 368, 172 S.E.2d 535, 540 (1970).
One crime is a lesser included offense of another if all the essential elements of the lesser offense are also essential elements of the greater offense. State v. Hudson, 345 N.C. 729, 732, 483 S.E.2d 436, 439 (1997). An “essential element” of a crime is a fact that must be proved beyond a reasonable doubt to convict a defendant of that crime.
*178The crime of arson is the willful and malicious burning of the dwelling house of another person. State v. Vickers, 306 N.C. 90, 99-100, 291 S.E.2d 599, 606 (1982), overruled on other grounds by State v. Barnes, 333 N.C. 666, 430 S.E.2d 223, cert. denied, 510 U.S. 946, 126 L. Ed. 2d 336 (1993). Here, “dwelling house” means an inhabited house. Vickers, 306 N.C. at 100, 291 S.E.2d at 606. Thus, it is an essential element of the crime of arson that the burned house be inhabited.
Obviously, it is not an essential element of arson that the burned house be uninhabited. It is an essential element of the crime of burning an uninhabited house that the house be uninhabited. See G.S. § 14-62; State v. Gulley, 46 N.C. App. 822, 824, 266 S.E.2d 8, 9 (1980). Proof beyond a reasonable doubt that the house was uninhabited when it was burned is required to convict a defendant of burning an uninhabited house in violation of G.S. 14-62. Because defendant’s indictment did not charge him with all the elements of burning an uninhabited house, his conviction of that crime must be vacated.
[2] We disagree with defendant, however, that he should have a new trial on the charge of first-degree murder. The jury was presented with two theories of first-degree murder: murder committed with premeditation and deliberation, and murder committed in the perpetration of a felony in which a deadly weapon was used. See N.C. Gen. Stat. § 14-17 (Cum. Supp. 1997). It convicted defendant on both theories. Defendant assigns error to the trial court’s jury instruction on the felony murder rule, and to its failure to instruct on second-degree murder as a lesser included offense of first-degree murder with premeditation and deliberation.
We need not reach defendant’s argument regarding the felony murder rule, because defendant’s conviction predicated on the theory of murder with premeditation and deliberation was without error.
Second-degree murder is a lesser included offense of first-degree premeditated and deliberate murder; it lacks the elements of premeditation and deliberation. See G.S. § 14-17. Due process requires an instruction on a lesser included offense only if a jury could rationally find the defendant guilty of the lesser offense and not guilty of the greater. Hopper v. Evans, 456 U.S. 605, 611, 72 L. Ed. 2d 367, 373 (1982); State v. Larry, 345 N.C. 497, 516-18, 481 S.E.2d 907, 919, cert. denied, - U.S. -, 139 L. Ed. 2d 234 (1997). Whether a jury instruction on second-degree murder was required in this case depends on *179the quality of the evidence supporting the elements of premeditation and deliberation.
“Premeditation means that the act was thought out beforehand for some length of time, however short. . ." State v. Conner, 335 N.C. 618, 635, 440 S.E.2d 826, 835 (1994), cert. denied, — U.S. -, 139 L. Ed. 2d 134 (1997). “Deliberation means an intent to kill, carried out in a cool state of blood, in furtherance of a fixed design for revenge or to accomplish an unlawful purpose and not under the influence of a violent passion, suddenly aroused by lawful or just cause or legal provocation.” Id. at 635, 440 S.E.2d at 836.
In this case, defendant presented little more than alibi evidence. He claimed he was elsewhere, alone, when the murder occurred. There was eyewitness evidence to the contrary. This evidence depicts defendant as walking calmly and deliberately toward Waymon Gore’s mobile home with a rifle in one hand and a jugful of unidentified liquid in the other. Defendant walked right by Florence Gore and into the mobile home. Florence heard no altercation. She heard only Waymon’s cry, “No, don’t!” followed by a loud thud. Seconds later, as calmly and deliberately as he came, defendant walked away with the rifle in his hand. As the mobile home quickly became engulfed in a fire accelerated by some liquid fuel, defendant turned back to have a look before he went on his way. The evidence further showed that defendant killed Waymon Gore in an uncommonly vicious manner.
This evidence establishes that defendant acted with premeditation and deliberation when he murdered Waymon Gore. In the face of all the circumstantial evidence of premeditation and deliberation, the fact that defendant and Waymon Gore may have had a prior friendly relationship, standing alone, did not warrant an instruction on second-degree murder. This is particularly so because defendant’s case rested entirely on an alibi defense. See State v. Larrimore, 340 N.C. 119, 157-58, 456 S.E.2d 789, 809-10 (1995).
[3] Finally, defendant argues that the trial judge impermissibly expressed an opinion during the trial, that the trial court’s statements undermined the credibility of defendant’s evidence, and that a new trial is required. The statements in question were made by the trial judge when he sustained objections by the State to the introduction of hearsay statements, of which defendant was the declarant, by witnesses for the defense. The trial court explained that it was sustaining the objections because the statements that the defense attempted *180to elicit were “self[-]serving.” On two occasions, the trial judge offered more elaborate explanations to the jury:
Ladies and Gentlemen of the Jury, we have a rule of evidence in respect to declarations by the Defendant, at least at this stage of the trial, that is commonly described as being self serving [sic]. And those objections are sustained on that rule of evidence.
Ladies and Gentlemen of the Jury, let me explain to you the rule — self serving [sic] rule just for your benefit, because there have been numerous rulings on that.
The rule of evidence of self serving [sic] declarations of a Defendant is based upon the theory of not permitting a Defendant to place evidence of his position through third parties because those statements or declarations would not be subject to examination by the opposing side. And that’s the underlying theory behind it.
The propriety of the court’s evidentiary rulings is not before us. It is the statements made by the trial court in connection with those rulings which, defendant claims, characterized his declarations as “self[-]serving,” undermined his credibility and the credibility of all the defendant’s evidence, and unfairly prejudiced him.
The trial court made several evidentiary rulings by uttering little more than the phrase, “self[-]serving.” When the trial judge gave the jury a more detailed explanation of his rulings, he made it clear that they were based on a purported rule of evidence, the rule of evidence of self-serving declarations of defendants. We find no reasonable possibility that defendant would have been acquitted had the trial judge not said, “self[-]serving.” See N.C. Gen. Stat. § 15A-1443 (1997).
Defendant’s conviction of burning an uninhabited house, 96 CRS 1413, is vacated.
No error as to defendant’s conviction of first-degree murder, 96 CRS 1412.
Judges EAGLES and HUNTER concur.