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Theorem pm2.65da 587
Description: Deduction rule for proof by contradiction. (Contributed by NM, 12-Jun-2014.)
Hypotheses
Ref Expression
pm2.65da.1 ((𝜑𝜓) → 𝜒)
pm2.65da.2 ((𝜑𝜓) → ¬ 𝜒)
Assertion
Ref Expression
pm2.65da (𝜑 → ¬ 𝜓)

Proof of Theorem pm2.65da
StepHypRef Expression
1 pm2.65da.1 . . 3 ((𝜑𝜓) → 𝜒)
21ex 108 . 2 (𝜑 → (𝜓𝜒))
3 pm2.65da.2 . . 3 ((𝜑𝜓) → ¬ 𝜒)
43ex 108 . 2 (𝜑 → (𝜓 → ¬ 𝜒))
52, 4pm2.65d 586 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem is referenced by:  condandc  775  nelrdva  2743  frirrg  4084  prodgt0  7794  ixxdisj  8739  icodisj  8827  ltabs  9561
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