Theorem pm2.65d 655

Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994.) (Proof shortened by Wolf Lammen, 26-May-2013.)

Hypotheses

Ref	Expression
pm2.65d.1	|- ( ph -> ( ps -> ch ) )
pm2.65d.2	|- ( ph -> ( ps -> -. ch ) )

Assertion

Ref	Expression
pm2.65d	|- ( ph -> -. ps )

Proof of Theorem pm2.65d

Step	Hyp	Ref	Expression
1		pm2.65d.2	. . 3 |- ( ph -> ( ps -> -. ch ) )
2		pm2.65d.1	. . 3 |- ( ph -> ( ps -> ch ) )
3	1, 2	nsyld 643	. 2 |- ( ph -> ( ps -> -. ps ) )
4	3	pm2.01d 613	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 609  ax-in2 610

This theorem is referenced by:  pm2.65da  656  mtod  658