Ketubot, Chapter Two, Mishnah Eight
In this mishnah three tannaim debate whether the testimony of a single witness is sufficient to confirm that an unknown person is a priest.
1) Rabbi Judah says: one does not raise [a person] to the priesthood through the testimony of one witness.
2) Rabbi Elazar says: When is this true? When there are people who object; but when there are no people who object, one raises [a person] to the priesthood through the testimony of one witness.
3) Rabbi Shimon ben Gamaliel says in the name of Rabbi Shimon the son of the assistant chief of priests: one raises [a person] to the priesthood through the testimony of one witness.
Section one: Rabbi Judah disagrees with yesterdays mishnah in which we learned that one person is believed to testify that another person is a priest.
Section two: Rabbi Elazar limits Rabbi Judahs statement to a case in which other people protest that so-and-so is not a kohen. In that type of situation two witnesses are necessary to raise someone to the priesthood. However, in the absence of others protesting, one witness is believed to say that someone else is a kohen.
Section three: Rabbi Shimon ben Gamaliel agree with the opinion in the previous mishnah according to which a person is always believed to say that a person is a priest.
We should note that determining whether a person was a priest must have been an issue of importance and difficulty after the destruction of the Temple. When the Temple stood, everyone pretty much knew who the priests were, because they were descendents of those who served regularly in the Temple. Furthermore, when the Temple was destroyed, the records kept in the Temple were probably lost. Hence testimony about a persons being a priest became scarcer and hence more essential.