Theorem pm2.01da 645

Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

Ref	Expression
pm2.01da.1	|- ( ( ph /\ ps ) -> -. ps )

Assertion

Ref	Expression
pm2.01da	|- ( ph -> -. ps )

Proof of Theorem pm2.01da

Step	Hyp	Ref	Expression
1		pm2.01da.1	. . 3 |- ( ( ph /\ ps ) -> -. ps )
2	1	ex 115	. 2 |- ( ph -> ( ps -> -. ps ) )
3	2	pm2.01d 627	1 |- ( ph -> -. ps )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-in1 623

This theorem is used by:  efrirr  4498  infnfi  7199  fun2dmnop0  11302  4sqlem18  13187  uhgr2edg  16447