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The Bavli, Shabas 37 amud 1, wonders about the permissibility of placing a pot of food adjacent to a stove-oven (rather than atop or in it) when the stove-oven has good fuel in it that has not been cooled. Its second attempted proof succeeds in proving that one may not do so. It then asks "What is the result?" and proceeds to bring another proof (that one may do so). Why doesn't it accept the valid proof of impermissibility?

The proof is as follows: Rav Chiya says a cooled oven that then caught fire again can have a pot of food placed near it. The implication is that an oven that has not been cooled (which is our question) cannot have a pot of food placed near it. (Attempts to discredit that implication by arguing that the case was mentioned by the way and not specifically — and so cannot be inferred from — are refuted.)

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    not an answer but a resource. If you go to dafyomi.co.il you can send questions like this to the kollel and they will email an answer. – rosends Oct 5 '14 at 22:42
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The Sefas Emes here says that the gemora continued to investigate because the refutation only succeeded in showing that the argument that the case was mentioned only incidentally was flawed, but maybe the assertion is still true anyway even without the attempted proof.

Thus, this is the sequence of the gemora:

The gemora asks about the permissibility of placing a pot of food adjacent to a stove-oven which has not been cooled.

The gemora brings a teaching of Rav Safra in the name of Rav which seems to say that it is forbidden.

The gemora attempts to reject this conclusion by asserting that the case of placing a pot of food adjacent to a stove-oven was only mentioned incidentally in the teaching, and tries to prove this assertion from the other cases in the teaching.

The gemora argues that this proof is flawed.

The gemora then continues to investigate because although the proof to the assertion that the case was mentioned incidently was flawed, maybe the assertion is true anyway even without the attempted proof.

The gemora concludes from another teaching that placing a pot of food adjacent to a stove-oven which has not been cooled is clearly permitted, and thus the assertion concerning the other teaching - that it was mentioned only incidentally - was correct.

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