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The Mishna (Ketubot 2:10, 28a) states that there are certain people who are trusted to deliver testimony that relates to something that they witnessed as minors. Included within that list are those who testify concerning the handwriting of their father, their rabbi and their brother.

The gemara (Ketubot 28a) asks why it is necessary to teach all three (father, rabbi, brother), and resolves that if it only mentioned one's father we would not be able to deduce one's rabbi, that if it only mentioned one's rabbi we would not be able to deduce one's father, and that even if it mentioned one's father and one's rabbi we would still not be able to deduce one's brother.

The problem is that, while one's father and one's brother have aspects to them that mean they need to be taught independently of one another, that which allows one to testify concerning his brother's handwriting should go for the other two as well!

Specifically, the reason that one can be trusted to recognise his father's handwriting is that he was commonly found around his father as a child, which is not the case with one's rabbi, and the reason that he is trusted to recognise his rabbi's handwriting is that he was in awe of him, which is not the case with one's father. But the reason that he is trusted to recognise his brother's handwriting is that testifying to somebody's handwriting is only a rabbinic obligation, and so we can be lenient!

I understand why you cannot deduce the third scenario from the first two, but it seems to me that you can deduce the first two from the third. Teach the case of the brother then - why do you need to also teach the case of one's father and one's rabbi!?

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Ritva explains simply that the Mishnah is using the technique of lo zu af zu. That is to say that indeed the Mishnah could have only mentioned the case of a brother and we would know the law for a father and a teacher as well, but mishnayot sometimes list multiple cases in increasing order of novelty even when it would suffice to only list the most novel case.

אבל אחיו דלא הא ולא הא אימא לא קמ"ל פירוש ומתני' לא זו אף זו קתני ומסתברא דכיון דקתני אחיו דלא הא ולא הא ה"ה לאדם רחוק דעלמא דמאי שנא ותנא דמתני' נקט הנהו דמסתמא שכיח גבייהו וידע כתבא דידהו

A possible answer that does not rely on mere stylistic choice is the following, loosely based on R. Yaakov Gezundheit's comments in Tiferet Yaakov C.M. 46:30.

The Talmud's conclusion — based on the fact that the Mishnah included one's brother in the list of people whose handriting he can verify — is that the reason why the person is trusted to verify the handwriting is that the verification is only a rabbinic requirement, so the Rabbis can make whatever rules they want for their own requirements. However, if the Mishnah had only mentioned that one can verify the handwriting of his brother, we would not necessarily have known the full extent of this rule. We might have thought that the reason one can verify his brother's handwriting is that he is (somewhat) familiar with his brother, but perhaps we would not trust him to verify the handwriting of someone not related to him at all.

This potential misunderstanding is avoided by including the father and the teacher in the list. We can no longer think that the reason why he is trusted to verify his brother's handwriting is that there is some unique familiarity with one's brother, because if that was the case then there would have been no need to list the father and teacher. By first listing the father and teacher and then listing the brother the Mishnah provides a contrast and tells us that a person is trusted to verify the handwriting of his brother even though he is less familiar with his brother. Thus, we can figure out that the reason is that the Rabbis can make up whatever rules they want for rabbinic requirements, and therefore it would turn out that he is trusted to verify anyone's handwriting. Note that this point itself is a dispute mentioned in Shulchan Aruch (C.M. 46:17).

(Of course, this explanation doesn't address why the Mishnah didn't just say explicitly that he is trusted to verify anyone's handwriting, if that is really true, but that wasn't the question asked here.)

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