Theorem pm2.65 134

Description: Theorem *2.65 of [WhiteheadRussell] p. 107. Proof by contradiction.

Assertion

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

Proof of Theorem pm2.65

Step	Hyp	Ref	Expression
1		pm3.2im 122	. . 3 |- (ph -> (ps -> -. (ph -> -. ps)))
2	1	a2i 9	. 2 |- ((ph -> ps) -> (ph -> -. (ph -> -. ps)))
3	2	con2d 91	1 |- ((ph -> ps) -> ((ph -> -. ps) -> -. ph))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  pm2.65i 135  pm2.65d 136  pm5.18 660  pm4.82 739

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

Copyright terms: Public domain