PER CURIAM.

Earl Lavann Reese appeals the denial of his 28 U.S.C. § 2254 habeas corpus petition by the United States District Court for the Eastern District of Missouri. 1 For reversal Reese contends that the state prosecutor suppressed exculpatory evidence in the form of an arrest warrant, that his trial counsel was incompetent in failing to discover and use the warrant, that his appellate counsel was incompetent for failing to raise the warrant issue on direct appeal, and that he was entitled to an evidentiary hearing on his habeas petition. We affirm.

Shortly after a robbery in Kansas City, police found what they believed to be the getaway car parked in front of the home of Ms. Shekena Dabner, Reese’s girlfriend. A police officer knocked on the door and asked Ms. Dabner a few questions. According to the officer, Ms. Dabner consented to a warrantless search of her home. The search revealed several items from the robbery and it also revealed Reese hiding in a crawl space in the attic. The officer then made a warrantless arrest of Reese. In a pretrial suppression hearing in the Circuit Court of Jackson County, Missouri, the warrantless search and arrest were found to have been proper. Reese was convicted by a jury of robbery in the first degree under Mo.Rev.Stat. § 569.020.

At the sentencing hearing, the judge discovered an arrest warrant for Reese in the court file. The warrant was for the same charge of robbery in the first degree and it was issued on the same day as Reese’s warrantless arrest. The return on the warrant was signed by a different officer than the one who arrested Reese at Ms. Dab-ner’s home. The judge found that the warrant was a matter to be taken up by the appellate court, and Reese was sentenced to life imprisonment as a dangerous offend *350 er pursuant to Mo.Rev.Stat. §§ 558.016 and 557.036.3.

The warrant issue was not raised by Reese in his direct appeal, see State v. Reese, 625 S.W.2d 130 (Mo.1981), and he was not allowed to raise it in a subsequent appeal. Having exhausted all of his state remedies, Reese filed a 28 U.S.C. § 2254 habeas corpus petition with the United States District Court for the Eastern District of Missouri. Reese claimed that the arrest warrant constituted exculpatory evidence suppressed by the prosecutor, that his trial counsel was incompetent for not discovering the warrant and using it to impeach the officer who made the warrant-less arrest, and that his appellate counsel was incompetent for not raising the warrant issue on direct appeal. Pursuant to the Review and Recommendation of the United States Magistrate, 2 the court denied Reese’s habeas petition. This appeal followed.

We note at the outset that Reese contends that we should remand this case for an evidentiary hearing on his claims. In support of this contention he recites several questions of fact regarding the arrest warrant which he says remain unresolved. “A habeas corpus petition may be properly dismissed without a hearing where facts are not in dispute or where the dispute can be resolved on the basis of the record.” Riley v. Lockhart, 726 F.2d 421, 423 (8th Cir.1984). The issues in Reese’s habeas petition can be resolved using only the undisputed facts in the limited record. The resolution of the factual disputes referred to by Reese would have no impact on the result, and a hearing therefore is not required. See Hill v. Lockhart, 731 F.2d 568, 573 (8th Cir.1984), aff'd, — U.S. -, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985).

Reese first argues that the arrest warrant was exculpatory material and that the prosecutor failed to disclose its existence to him. “[T]he suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution.” Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 1196-97, 10 L.Ed.2d 215 (1963). Three things must be shown in order to make out a Brady claim: “the suppression of evidence, the evidence’s favorable character to the accused, and the evidence’s materiality.” United States v. Smith, 538 F.2d 1332, 1334 (8th Cir.1976). We find that Reese has failed to make any of these showings.

It is unclear whether Reese made an evidentiary request to the prosecutor which would have covered the arrest warrant. Nevertheless, the court file in which the warrant was found was readily available to Reese and his attorney, and it can hardly be said that the prosecutor suppressed the warrant or failed to disclose its existence.

We also cannot find that the evidence was exculpatory and material. Reese claims that he would have used the warrant to impeach the officer who made the warrantless search and arrest. “When the ‘reliability of a given witness may well be determinative of guilt or innocence,’ nondisclosure of evidence affecting credibility falls within [the Brady ] rule.” Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972) (quoting Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 1177, 3 L.Ed.2d 1217 (1959)). Had the officer’s credibility been impeached, the trial court possibly might have ruled that the warrantless search and arrest were illegal. This could have led to dismissal of the charges against Reese. However, it is very difficult to see how the arrest warrant could have reflected adversely on the officer’s character. Even if the warrant had been issued shortly after the crime occurred, its existence would have had no bearing on the propriety of the subsequent warrantless search and arrest. 3 *351 Indeed, no matter what the facts regarding the warrant were, its existence was irrelevant to the officer’s credibility or to the propriety of his warrantless search and arrest.

The materiality test for Brady material was recently reformulated by the Supreme Court in United States v. Bagley, — U.S. -, 105 S.Ct. 3375, 3384, 87 L.Ed.2d 481 (1985), to conform with the prejudice test for incompetence of counsel in Strickland v. Washington, 466 U.S. 668, 694, 104 S.Ct. 2052, 2068, 80 L.Ed.2d 674 (1984).

The evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different. A “reasonable probability” is a probability sufficient to undermine confidence in the outcome.

Bagley, 105 S.Ct. at 3384. This test is applicable to “no request,” “general request” and “specific request” situations. Id. The probability of a different outcome in Reese’s case is practically nonexistent and certainly is not sufficient to undermine our confidence in his conviction. We therefore find that Reese’s Brady argument has no merit.

We are equally unpersuaded by Reese’s incompetence of counsel arguments. Reese must show first that “counsel made errors so serious that counsel was not functioning as the ‘counsel’ guaranteed ... by the Sixth Amendment.” Strickland, 466 U.S. at 687, 104 S.Ct. at 2064. Second, Reese must show that his defense was prejudiced by the errors. Id. Proof of prejudice requires a showing “that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. at 2068.

Reese contends that his trial counsel was incompetent for failure to investigate the existence of a warrant, and for failure to discover the warrant and use it at trial. From our previous conclusion that the existence of the warrant was not material for Brady purposes, it follows by using the same standard that trial counsel’s failure to investigate and to discover and use the warrant was not prejudicial. Failure to investigate the existence of a warrant was not prejudicial because the order for warrant, the warrant and the return, all dated the same day as Reese’s warrantless arrest, reflect full compliance with the requirements of Mo. S.Ct. R. 22.06. Failure to discover the warrant and use it at trial was not prejudicial because the warrant was irrelevant to the propriety of the war-rantless search and arrest and to the credibility of the arresting officer. Therefore, there is not a reasonable probability that, absent the alleged errors, the result of Reese’s trial would have been different.

Reese also alleges that his appellate counsel was incompetent for not raising the Brady issue on his direct appeal. This failure precluded him from raising the issue in any subsequent state proceeding. It is well settled that a criminal, defendant is entitled to effective assistance of counsel on his first appeal as of right. See Beavers v. Lockhart, 755 F.2d 657, 661 (8th Cir.1985). We have held, however, that a defendant cannot be prejudiced “unless the issue omitted by appellate counsel had arguable merit.” Parton v. Wyrick, 704 F.2d 415, 416 (8th Cir.1983). Reese’s Brady issue did not have arguable merit and there is no reasonable probability that his direct appeal would have been successful had the issue been submitted. We therefore cannot find that Reese was prejudiced by the omission of his appellate counsel.

Accordingly, the denial of Reese’s habeas corpus petition by the district court is affirmed.

Notes

. The Honorable Stephen N. Limbaugh, United States District Judge, Eastern District of Missouri.

. The Honorable William S. Bahn, United States Magistrate, Eastern District of Missouri.

. Since the warrantless arrest took place "an hour or so” after the robbery, it is highly unlikely that the warrant was issued before Reese was *351 arrested. The State speculates that the warrant was issued in order to comply with Mo. S.Ct. R. 22.06, which provides:

Any person arrested without a warrant and confined in any place for the alleged commission of any felony shall be discharged from custody within twenty hours from the time of such arrest unless he be held upon a warrant.