Theorem pm2.8 800

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		pm1.4 717	. . 3 |- ( ( ph \/ ps ) -> ( ps \/ ph ) )
2	1	ord 714	. 2 |- ( ( ph \/ ps ) -> ( -. ps -> ph ) )
3	2	orim1d 777	1 |- ( ( ph \/ ps ) -> ( ( -. ps \/ ch ) -> ( ph \/ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)