Theorem pm2.8 723

Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.8	|- ( ( ph \/ ps ) -> ( ( -. ps \/ ch ) -> ( ph \/ ch ) ) )

Proof of Theorem pm2.8

Step	Hyp	Ref	Expression
1		pm1.4 646	. . 3 |- ( ( ph \/ ps ) -> ( ps \/ ph ) )
2	1	ord 643	. 2 |- ( ( ph \/ ps ) -> ( -. ps -> ph ) )
3	2	orim1d 701	1 |- ( ( ph \/ ps ) -> ( ( -. ps \/ ch ) -> ( ph \/ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)