Sanhedrin 23B

ואמר רב דימי בריה דרב נחמן בריה דרב יוסף: כגון דקבליה עליה בחד.

And Rav Dimi, son of Rav Naḥman, son of Rav Yosef, says: This is referring to a case where the litigant accepted one of these people upon himself as one of the judges, in addition to two fit judges. Since the dispute between R' Meir and the Rabbis with regard to a litigant retracting his acceptance of someone who is generally disqualified from judging is stated in the next Mishnah, why is it stated in this Mishnah as well?

צריכא, דאי תנא ״אבא״ ו״אביך״⁠ – בהא קאמרי רבנן דלא מצי הדר ביה, משום דאבא ואביך חזו לעלמא. אבל חד כבי תרי, דלעלמא לא חזי ⁠– אימא: מודו ליה לרבי מאיר.

The Talmud answers: The statements in both mishnayot are necessary. As, had the Mishnah taught this dispute only with regard to a litigant who said: My father is trusted to adjudicate for me, or: Your father is trusted to adjudicate for me, one might have reasoned that only in this case did the Rabbis say that he cannot retract his acceptance, because: My father, and: Your father, are fit to judge for the general public. But in a case where a litigant accepts one witness as equivalent to two witnesses, since one witness is someone who is not fit to testify by himself for the general public one might say that the Rabbis concede to R' Meir that he can retract his acceptance. Therefore, it is necessary for the dispute to be stated with regard to the case in this Mishnah as well.

ואי אשמעינן בהא, בהא קאמר רבי מאיר, אבל בההיא ⁠– אימא מודו להו לרבנן. צריכא.

And conversely, if the Mishnah would teach us their dispute only with regard to this case, where a litigant effectively accepted one witness as equivalent to two, one might have reasoned that specifically in this case R' Meir says that he can retract his acceptance. But in that case, where he accepted his father or the father of the other litigant as a judge, one might say that R' Meir concedes to the Rabbis that he cannot retract his acceptance. It is therefore necessary for the Mishnah to state both disputes.