
438 So.2d 864 (1983)
Leonard SPENCER, Appellant,
v.
STATE of Florida, Appellee.
No. AQ-185.
District Court of Appeal of Florida, First District.
September 7, 1983.
Rehearing Denied October 26, 1983.
*865 Carl S. McGinnes, Asst. Public Defender, Tallahassee, for appellant.
Jim Smith, Atty. Gen., and David P. Gauldin, Asst. Atty. Gen., for appellee.
SHIVERS, Judge.
Spencer appeals his convictions and sentences for armed robbery and unlawful display of a firearm during the commission of a felony. Although we find no merit in appellant's contention that the double jeopardy clause bars his prosecution for these *866 offenses, we find that appellant was improperly convicted and sentenced for both the greater and lesser included offense. We affirm in part and reverse in part.
Spencer was accused of robbing a gas station while using a pistol on August 25, 1982. A two-count felony information was filed against him. Count I alleged armed robbery, contrary to section 812.13(2)(a), Florida Statutes (1981). Count II alleged that appellant unlawfully displayed a pistol firearm while committing a felony, contrary to section 790.07(2), Florida Statutes (1981).
A separate misdemeanor charge of being in possession of a firearm with an altered or removed serial number was brought against appellant, and on September 23, 1982, appellant pled guilty in county court to this charge. On October 21, 1982, appellant filed a motion to dismiss the felony charges, asserting that principles of double jeopardy precluded his prosecution on the other charges. At the hearing on the motion to dismiss, Officer Streeter testified that on August 25, 1982, he received a BOLO for a black male who had allegedly just perpetrated an armed robbery at a service station. Streeter proceeded to a location near the service station where Officer Bolger had stopped a vehicle. Appellant and another person were occupying the vehicle and were taken into custody. A hat and a gun were discovered inside the stopped vehicle. The serial number on the gun was obliterated. The victim identified appellant as being the robber and also identified the hat and gun as being utilized during the offense.
The trial court denied appellant's motion to dismiss, and appellant pled nolo contendere on both felony charges, reserving his right to appeal the denial of the motion to dismiss. Appellant was adjudicated guilty and sentenced to 20 years on Count I with the requirement that he serve three years before being considered for parole. Appellant was also convicted on Count II and sentenced to ten years imprisonment to run concurrently with the sentence on Count I.
The double jeopardy clause has three major facets. It protects against a second prosecution for the same offense after acquittal, against a second prosecution for the same offense after conviction, and against multiple punishments for the same offense. North Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969). The classic test for determining whether two separate statutory offenses are the "same offense" for double jeopardy purposes was enunciated in Blockburger v. United States, 284 U.S. 299, 52 S.Ct. 180, 76 L.Ed. 306 (1932). The test is "whether each provision requires proof of an additional fact which the other does not." Id. at 304, 52 S.Ct. at 182. Sub judice, appellant admits that the crime to which he pled guilty in the first prosecution, possession of a firearm with an altered or removed serial number, is not the same offense under the Blockburger test as either of the crimes involved in the subsequent prosecution, armed robbery and display of a firearm while committing a felony. Nevertheless, appellant argues that principles of collateral estoppel should bar his subsequent prosecution.
It is true that collateral estoppel  the principle that bars relitigation between the same parties of issues determined at a previous trial  is a part of criminal as well as civil law. It is also true that the doctrine of collateral estoppel is an ingredient of the fifth amendment guarantee against double jeopardy. Ashe v. Swenson, 397 U.S. 436, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970). In the instant case, appellant argues that the fact of his possession of a firearm was resolved in the initial prosecution for possession of a firearm with an altered or removed serial number. Possession of a firearm is also an element of the crimes of armed robbery and display of a firearm while committing a felony. Appellant reasons that the doctrine of collateral estoppel bars the State from relitigating this issue, and, therefore, the State cannot prove its case in the subsequent felony prosecution.
Appellant, however, overlooks the fact that in the initial prosecution the issue *867 of possession of a firearm was decided against him. The theory of collateral estoppel, as applied in criminal cases, requires that when an issue in a criminal trial is determined in a way favorable to the defendant the State is estopped from raising that issue in a subsequent prosecution. United States v. Venable, 585 F.2d 71 (3d Cir.1978). All of the collateral estoppel cases cited involve situations where the outcome of previous litigations necessarily involved the resolution of an issue in a way favorable to the defendant. See Ashe v. Swenson, supra, and cases cited therein; Gragg v. State, 429 So.2d 1204 (Fla. 1983). Logically, if the doctrine of collateral estoppel were applied in appellant's case, the State would not need to prove possession of the firearm in appellant's subsequent prosecution because that issue was conclusively determined against appellant in the prior prosecution. The fact that the State cannot do that very thing is referred to as a lack of "mutuality" in the use of the doctrine of collateral estoppel in the criminal law. See United States v. DeAngelo, 138 F.2d 466 (3d Cir.1943). Although the State cannot use collateral estoppel to prove elements of its case which have previously been determined in a way adverse to the defendant in a prior trial, there is no reason why the State should be estopped from proving these facts again in a subsequent prosecution unless the prior conviction was for "the same offense."
We have not overlooked appellant's argument that In Re Nielsen, 131 U.S. 176, 9 S.Ct. 672, 33 L.Ed. 118 (1889), is applicable to the instant case. Nielsen held that a conviction of a Mormon on a charge of cohabiting with his two wives over a two and one-half year period barred a subsequent prosecution for adultery with one of those wives on the day following the end of that period. The Supreme Court discussed Nielsen in a footnote in Brown v. Ohio, 432 U.S. 161, 97 S.Ct. 2221, 53 L.Ed.2d 187 (1977), and pointed out that a strict application of the Blockburger test would have permitted the subsequent prosecution. 432 U.S. at 166-67, n. 6, 97 S.Ct. at 2226, n. 6. Nielsen, however, is not a case where the doctrine of collateral estoppel was applied. Rather, the Court in Nielsen thought that the crime of adultery was the "same offense" as cohabitation even though the crimes of adultery and cohabitation each technically included an element the other did not.[1] In the instant case, it cannot be said that possession of a firearm with an altered or removed serial number is the same offense as armed robbery or display of a firearm while committing a felony.
Appellant's conviction for display of a firearm while committing a felony, however, must be reversed. That crime is a lesser included offense of armed robbery in situations where, as here, the two crimes arise out of a single transaction. State v. Gibson, 8 FLW 76 (Fla. 1983). Appellant cannot be convicted or sentenced for both a greater and lesser included offense. Bell v. State, 437 So.2d 1057 (Fla. 1983).
*868 Accordingly, appellant's conviction and sentence for armed robbery is affirmed. His conviction for display of a firearm while committing a felony is reversed, and the sentence is vacated.
ROBERT P. SMITH, Jr. and NIMMONS, JJ., concur.
NOTES
[1]  The Court stated:

[C]an it be doubted that the adultery charged in the second indictment was an incident and part of the unlawful cohabitation? We have no doubt of it. True, in the case of Snow, we held that it was not necessary to prove sexual intercourse in order to make out a case of unlawful cohabitation; that living together as man and wife was sufficient; but this was only because proof of sexual intercourse would have been merely cumulative evidence of the fact. Living together as man and wife is what we decided was meant by unlawful cohabitation under the statute. Of course, that includes sexual intercourse. And this was the integral part of the adultery charged in the second indictment, and was covered by and included in the first indictment and conviction. The case was the same as if the first indictment had in terms laid the unlawful cohabitation for the whole period preceding the finding of the indictment. The conviction on that indictment was in law a conviction of a crime which was continuous, extending over the whole period, including the time when the adultery was alleged to have been committed. The petitioner's sentence, and the punishment he underwent, on the first indictment, was for that entire, continuous crime. It included the adultery charged. To convict and punish him for that also was a second conviction and punishment for the same offense.
131 U.S. at 187, 9 S.Ct. at 675.
