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Theorem pm2.01d 548
Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
pm2.01d.1 (φ → (ψ → ¬ ψ))
Assertion
Ref Expression
pm2.01d (φ → ¬ ψ)

Proof of Theorem pm2.01d
StepHypRef Expression
1 pm2.01d.1 . 2 (φ → (ψ → ¬ ψ))
2 pm2.01 546 . 2 ((ψ → ¬ ψ) → ¬ ψ)
31, 2syl 14 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
This theorem is referenced by:  pm2.01da  564  pm2.65d  585  pm5.19  621  mtord  696  swopo  4034  rennim  9211
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