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Does a get require witnesses to sign lishmah according to Rav Elazar? The Gemara (גמרא) infers from a braisa about three invalid gittin that Rav Elazar permits marriage lechatchilah even without witness signatures. Rashi (רש"י) and Tosafos (תוספות) differ on whether this proves no rabbinic requirement of lishmah exists, or whether witness signatures remain required lechatchilah though their absence doesn't invalidate the get.
This shiur analyzes Gittin 3b's discussion of whether witness signatures on a get require lishmah (intent for the specific divorce) according to Rav Elazar. The Gemara (גמרא) attempts to prove from a braisa discussing three types of invalid gittin that Rav Elazar holds there is no requirement of lishmah even mid'rabanan for witness signatures. The braisa lists three gittin that are pasul mid'rabanan but if the woman remarried we don't force her to divorce: (1) a get without witness signatures but with the husband's handwriting, (2) a get with witness signatures but without the husband's handwriting, and (3) a get written by a scribe with one witness. Rav Elazar is machshir (validates) these cases. The Gemara initially understands this to mean Rav Elazar permits marriage lechatchilah without witness signatures, proving he holds there's no din of lishmah even mid'rabanan.
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Gittin 3b
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