Theorem pm2.65d 166

Description: Deduction rule 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 132	. 2 |- (ph -> (ps -> -. ps))
4	3	pm2.01d 161	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-3 8

This theorem is referenced by:  mtod  168  pm2.65da  559