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Theorem pm2.01d 558
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  |-  ( ph  ->  ( ps  ->  -.  ps ) )
Assertion
Ref Expression
pm2.01d  |-  ( ph  ->  -.  ps )

Proof of Theorem pm2.01d
StepHypRef Expression
1 pm2.01d.1 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
2 pm2.01 556 . 2  |-  ( ( ps  ->  -.  ps )  ->  -.  ps )
31, 2syl 14 1  |-  ( ph  ->  -.  ps )
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 554
This theorem is referenced by:  pm2.01da  575  pm2.65d  596  pm5.19  632  mtord  707  swopo  4070  rennim  9828  absle  9915
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