Kesubos chapter 2, mishnah 7. In the previous mishnah we learned that two women who were taken captive are believed to testify about one another that she is pure and was not violated by a gentile, and therefore she is considered fit.
Our mishnah deals with a similar question: is a person's testimony about himself, "I am a kohen," enough to establish him as a kohen and to allow Terumah to be given to him? This is the discussion before us in this mishnah and in the one that follows.
The text of the mishnah:
"V'chein shnei anashim, zeh omer kohen ani v'zeh omer kohen ani" - and so too two men, each one of whom testifies about himself that he is a kohen.
"Einan ne'emanin" - a person is not believed about himself to say that he is a kohen, and Terumah is not given to him on the basis of such a statement.
"U'vizman shehein me'idin zeh es zeh - harei eilu ne'emanin" - when each one testifies about his fellow that he is a kohen, they are believed.
Although at first glance there is a concern here of 'gomel' - that each one says to his fellow: you testify about me and I will testify about you - the mishnah rules that they are believed, exactly as was explained regarding the captive women in the previous mishnah.
In summary: a person is not believed to testify about himself that he is a kohen, but two who testify about one another are believed, and we are not concerned about gomel, just as in the case of the two captive women in the previous mishnah.
However, already in the next mishnah we will see that this is not universally agreed upon.