Theorem pm3.45 605

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 336	1 |- ( ( ph -> ps ) -> ( ( ph /\ ch ) -> ( ps /\ ch ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  ssrmof  3311  rabss2  3331  lmtopcnp  15351