Theorem pm2.01d 580

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

Step	Hyp	Ref	Expression
1		pm2.01d.1	. 2 |- ( ph -> ( ps -> -. ps ) )
2		pm2.01 578	. 2 |- ( ( ps -> -. ps ) -> -. ps )
3	1, 2	syl 14	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 576

This theorem is referenced by:  pm2.01da  597  pm2.65d  618  pm5.19  654  mtord  729  swopo  4061  rennim  9888  absle  9975