In an indirect proof, is it possible to reject the assumption based on contradiction of a premise?

pigskiniv 2022-08-12 Answered
In an indirect proof, is it possible to reject the assumption based on contradiction of a premise?
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Answers (2)

Irene Simon
Answered 2022-08-13 Author has 16 answers
This is a proof that x A ¬ P. It can be simplified, since everything between "Assume P" and "Derive x A" is just a proof that P x A, from which by contrapositive we get x A ¬ P, which was to be demonstrated.
You can't in general conclude from this that P is always false, of course.

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brasocas6
Answered 2022-08-14 Author has 3 answers
Yes. Deriving a contradiction from the assumption of P is a proof for ¬ P.
Although apparently similar, this is not actually Reduction ad Absurdum.
This is the Rule of Negation Introduction. Unlike RAA this is an intuitionistically valid rule of inference.
Σ , ¬ P Σ ¬ ¬ P ¬ I Σ P ¬ ¬ E

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