Theorem pm3.45 592

Description: Theorem *3.45 (Fact) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.45	|- ( ( ph -> ps ) -> ( ( ph /\ ch ) -> ( ps /\ ch ) ) )

Proof of Theorem pm3.45

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	anim1d 334	1 |- ( ( ph -> ps ) -> ( ( ph /\ ch ) -> ( ps /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 103

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ssrmof  3210  rabss2  3230  lmtopcnp  13044