Gemara

(Rav Nachman): "Lo Yomas Al Pi Ed Echad" - Edus Meyuchedes (the witnesses did not see each other) is invalid for capital cases, but it is valid for monetary cases.

Question (Rav Zutra): (We use any reason to avoid Misas Beis Din.) If Edus Meyuchedes is valid in some case, we should validate it in capital cases when it will save lives! (If we can join witnesses who did not see together, if only one pair was Huzam, we should disqualify all the testimony!) Why does the Mishnah say that we kill the transgressor and the lying witnesses?

This is left difficult.

Sanhedrin 29a (Mishnah): If he says 'he himself told me' (this is invalid). He must say 'he admitted to Shimon in front of us that he owes him.'

(R. Chiya bar Aba): If the did not say 'you are witnesses against me', afterwards he can say that the admission was a joke.

30a (Beraisa): Witnesses can testify together only if they saw the testimony together;

R. Yehoshua ben Korchah says, we can join their testimony even if they saw it one after the other.

30b (R. Chiya bar Avin citing Rav, and Rav Yosef citing Ula): The Halachah follows R. Yehoshua ben Korchah, both for land and Metaltelim.

(Ula, and R. Zeira citing Rav): The Halachah follows R. Yehoshua ben Korchah regarding land, but not regarding Metaltelim.

(Rav): (Testimony of) different admissions join. An admission joins a loan before the admission. Different loans do not join, nor does an admission join a loan after the admission.

Question (Rav Nachman bar Yitzchak): Different loans do not join, for they do not testify about the same money. Likewise, different admissions should not join, for (perhaps) they are not about the same money!

Answer (Rav Huna brei d'Rav Yehoshua): The case is, when Reuven admitted in front of Almoni, he said 'I already admitted about this debt in front of Ploni.' (Later, he told Ploni that he admitted about it also in front of Almoni.)

Question (Rava): If so (Reuven must tell each witness that the other witness also knows about this loan), this is just like an admission after a loan! (If so, why did Rav consider these to be separate cases?!)

(Chachamim of Neharde'a): We join (testimony of) two admissions, two loans, or one of each (in either order).

This is like R. Yehoshua ben Korchah.

Bava Basra 40a (Rava): Admission is in front of two people. Kinyan (Chalipin) is in front of two. Kiyum (validation of) documents is in front of three.

Gitin 33b - Question: If one said 'all of you write and give a Get to my wife', does R. Shimon (ben Gamliel) allow him to cancel this in front of only one?

Answer (Beraisa - R. Shimon ben Gamliel): If one told two people 'give a Get to my wife,' he can cancel them only together. (Both must sign the Get, so it is as if he said 'all (i.e. both) of you')!

Rejection (Rav Ashi): The Beraisa discusses only giving the Get.

Support (Seifa): If he appointed each Shali'ach by himself, he can cancel each by himself. Sheluchim to write must be appointed together!

(Beraisa): Testimonies of witnesses combine only if they saw the matter together.

Rejection: Perhaps R. Shimon holds like R. Yehoshua ben Korchah.

Rishonim

Rif (Sanhedrin 9a) and Rosh (3:34): The Halachah follows R. Yehoshua ben Korchah. We join admissions, loans, or one of each, in either order.

Ba'al ha'Ma'or (Sanhedrin 7b DH Ad): The entire Mishnah is in the singular (he said to me...), except for 'he admitted in front of us.' This shows that an admission in front of one witness does not help. The witness cannot make him swear. He can say 'I was joking.' We say in Bava Basra that admission is in front of two, and Kiyum is in front of three. Just like Kiyum in front of less than three has no effect, also admission in front of less than two. We do not say that whenever two obligate money, one obligates an oath. His mouth obligates him, and not the witnesses. Therefore, he must be careful with his words, that they are not jest. Admission in front of less than two witnesses is not admission. Even though admission after admission joins (if he said that he admits to the same money he admitted to in front of Ploni), even though each was in front of only one witness, there is different, for in the end he admitted in front of two, so he was not joking. We do not claim for Reuven when (initially) Shimon claimed from him and Reuven admitted.

Milchamos Hash-m: The Gemara rejected the answer that he said that he admits to the same money he admitted to in front of Ploni, for this is like admission after a loan. The only reason we suggested this answer was to explain the difference between a loan after a loan and admission after admission (but not because one witness about an admission is nothing). Seemingly, according to Chachamim neither should join, and according to R. Yehoshua ben Korchah both should join! We conclude that even a loan after an admission joins, according to R. Yehoshua ben Korchah, even though there is only one witness about the admission! (If he told the latter witness about the admission, this is admission after admission!) Those who hold like the Ba'al ha'Ma'or must say that he admitted in front of two witnesses, but one went away and the other came to Beis Din (and he joins with the witness on the loan). There is no support for this. Bava Basra is no proof. Admission in front of two was taught next to Kinyan in front of two. It is clear from the Sugya of using a coin for Chalipin (Bava Metzia 46a) that Chalipin in front of one witness, or even without witnesses, is valid. The Yerushalmi says that if one was Moser an admission in front of one witness not in front of the lender, and all the more so in front of the lender. The Ba'al ha'Ma'or learned from the plural in the Mishnah 'he admitted in front of us.' Why didn't it disqualify 'he admitted in front of me'? Also according to me, the Mishnah should have taught that an admission without a prior claim is invalid even if it was in front of us! We must say that the Mishnah was not precise about this.

Rambam (Hilchos Edus 4:2): In monetary cases, even if the witnesses did not see each other, their testimony joins. If David says 'he lent (or admitted) to him in front of me on Yom Ploni' and Moshe says 'he lent (or admitted) to him in front of me on a different day,' their testimonies join.

Rambam (3): The same applies if one witness testifies about an admission and the other witness testifies that he saw a loan.

Poskim

Shulchan Aruch (CM 30:6): In monetary cases, even if the witnesses did not see each other, their testimony joins. If David says 'he lent to him in front of me on Yom Ploni' or 'he admitted to him in front of me on Yom Ploni,' and Moshe says 'he lent or admitted to him in front of me on a different day,' their testimonies join. The same applies if one witness testifies about an admission and the other witness testifies that he saw a loan.

Beis Yosef (DH Ein): The Rif, Rambam and Rosh say so. Semag disagrees, for Rav Ashi asked from Chachamim. Perhaps this is why Hagahos Maimoniyos and the Mordechai in the name of R. Tam and the Rashbam hold that admission after admission does not join. I disagree. Perhaps the Bnei Yeshiva (but not Rav Ashi) said that Sheluchim to write must be appointed together! Even if Rav Ashi said it, we do not abandon an explicit ruling where the matter was discussed due to a Diyuk elsewhere.

SMA (20): We join testimonies seen at different times, and all the more so Edus Meyuchedes, in which the witnesses saw the same event.

Rema: The same applies to testimony about an Isur.

Gra (23): The Yerushalmi says that we join witnesses who saw a Sotah secluded at different times, like R. Yehoshua ben Korchah.

Gra (EH 11:16): The Bavli connotes that R. Yehoshua ben Korchah argues even about Isurim, e.g. for Terumah and lineage (Kesuvos 26b, Bava Basra 32a) Gitin, and two hairs (Sanhedrin 30b).