Yevamot 46 - Conversion to Judaism
What is required to become Jewish? - All that is needed is for one to be circumcised, since that is what the Jews did in Egypt, as the verse states, " For all the people that went forth from Egypt were circumcised ." - this is the opinion of Rabbi Eliezer.
Rabbi Yehoshua says just the opposite: immersion in a mikvah is the only requirement, since this is all that Jewish women did, when they went out of Egypt. Obviously, they could not be circumcised, but how do we know that they indeed went to the mikvah? - Because if not that, how were they brought into the Divine presence? But, since it is impossible for a woman to be circumcised, how can we learn from that a law for a man? Rabbi Yehoshua says that we indeed can.
However, the Sages maintain that both circumcision and immersion in a mikvah are required. What is their logic? - They agree both with Rabbi Yehoshua and with Rabbi Eliezer and thus come up with both requirements.
Rav Safra tells a story how he was visiting Rabbi Chiya, with yet another Sage, and a convert came to them. He was circumcised but not immersed in a mikveh. Rabbi Chiya told him to wait until tomorrow morning, for then they would administer an immersion for him. We see three things from here: that both circumcision and immersion are required, that this immersion cannot be done at night, and that three people need to be present. Can we also derive that they all need to be Sages? - No, this is just how it happened.
Art: Jews at the Wailing Wall by Gustave Bauernfeind