Theorem pm2.81 801

Description: Theorem *2.81 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.81	|- ( ( ps -> ( ch -> th ) ) -> ( ( ph \/ ps ) -> ( ( ph \/ ch ) -> ( ph \/ th ) ) ) )

Proof of Theorem pm2.81

Step	Hyp	Ref	Expression
1		orim2 779	. 2 |- ( ( ps -> ( ch -> th ) ) -> ( ( ph \/ ps ) -> ( ph \/ ( ch -> th ) ) ) )
2		pm2.76 798	. 2 |- ( ( ph \/ ( ch -> th ) ) -> ( ( ph \/ ch ) -> ( ph \/ th ) ) )
3	1, 2	syl6 33	1 |- ( ( ps -> ( ch -> th ) ) -> ( ( ph \/ ps ) -> ( ( ph \/ ch ) -> ( ph \/ th ) ) ) )

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)