Theorem pm2.74 797

Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.74	|- ( ( ps -> ph ) -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ch ) ) )

Proof of Theorem pm2.74

Step	Hyp	Ref	Expression
1		idd 21	. . 3 |- ( ( ps -> ph ) -> ( ph -> ph ) )
2		id 19	. . 3 |- ( ( ps -> ph ) -> ( ps -> ph ) )
3	1, 2	jaod 707	. 2 |- ( ( ps -> ph ) -> ( ( ph \/ ps ) -> ph ) )
4	3	orim1d 777	1 |- ( ( ps -> ph ) -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ch ) ) )

Syntax hints:   -> 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-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)