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Theorem pm2.65d 585
Description: Deduction rule for proof by contradiction. (Contributed by NM, 26-Jun-1994.) (Proof shortened by Wolf Lammen, 26-May-2013.)
Hypotheses
Ref Expression
pm2.65d.1 (φ → (ψχ))
pm2.65d.2 (φ → (ψ → ¬ χ))
Assertion
Ref Expression
pm2.65d (φ → ¬ ψ)

Proof of Theorem pm2.65d
StepHypRef Expression
1 pm2.65d.2 . . 3 (φ → (ψ → ¬ χ))
2 pm2.65d.1 . . 3 (φ → (ψχ))
31, 2nsyld 576 . 2 (φ → (ψ → ¬ ψ))
43pm2.01d 548 1 (φ → ¬ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 544  ax-in2 545
This theorem is referenced by:  pm2.65da  586  mtod  588
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