Theorem pm2.76 797

Description: Theorem *2.76 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.76	|- ( ( ph \/ ( ps -> ch ) ) -> ( ( ph \/ ps ) -> ( ph \/ ch ) ) )

Proof of Theorem pm2.76

Step	Hyp	Ref	Expression
1		orc 701	. . 3 |- ( ph -> ( ph \/ ch ) )
2	1	a1d 22	. 2 |- ( ph -> ( ( ph \/ ps ) -> ( ph \/ ch ) ) )
3		orim2 778	. 2 |- ( ( ps -> ch ) -> ( ( ph \/ ps ) -> ( ph \/ ch ) ) )
4	2, 3	jaoi 705	1 |- ( ( ph \/ ( ps -> ch ) ) -> ( ( ph \/ ps ) -> ( ph \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 697

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-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm2.75  798  pm2.81  800  orimdidc  891  equs5or  1802