Theorem conax1k 644

Description: Weakening of conax1 643. General instance of pm2.51 645 and of pm2.52 646. (Contributed by BJ, 28-Oct-2023.)

Assertion

Ref	Expression
conax1k	|- ( -. ( ph -> ps ) -> ( ch -> -. ps ) )

Proof of Theorem conax1k

Step	Hyp	Ref	Expression
1		conax1 643	. 2 |- ( -. ( ph -> ps ) -> -. ps )
2	1	a1d 22	1 |- ( -. ( ph -> ps ) -> ( ch -> -. ps ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605

This theorem is referenced by:  pm2.51  645  pm2.52  646