Theorem impac 379

Description: Importation with conjunction in consequent. (Contributed by NM, 9-Aug-1994.)

Hypothesis

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

Assertion

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

Proof of Theorem impac

Step	Hyp	Ref	Expression
1		impac.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	ancrd 324	. 2 |- ( ph -> ( ps -> ( ch /\ ps ) ) )
3	2	imp 123	1 |- ( ( ph /\ ps ) -> ( ch /\ ps ) )

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 is referenced by:  imdistanri  444  f1elima  5752