Theorem imdistanri 446

Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.)

Hypothesis

Ref	Expression
imdistanri.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
imdistanri	|- ( ( ps /\ ph ) -> ( ch /\ ph ) )

Proof of Theorem imdistanri

Step	Hyp	Ref	Expression
1		imdistanri.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	com12 30	. 2 |- ( ps -> ( ph -> ch ) )
3	2	impac 381	1 |- ( ( ps /\ ph ) -> ( ch /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by: (None)