Theorem impac 651

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 577	. 2 |- ( ph -> ( ps -> ( ch /\ ps ) ) )
3	2	imp 445	1 |- ( ( ph /\ ps ) -> ( ch /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  imdistanri  727  f1elima  6520  zfrep6  7134  repswswrd  13531  sltval2  31809  bj-snsetex  32951