Theorem imdistanri 727

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 32	. 2 |- ( ps -> ( ph -> ch ) )
3	2	impac 651	1 |- ( ( ps /\ ph ) -> ( ch /\ ph ) )

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:  tc2  8618  prmodvdslcmf  15751  monmat2matmon  20629  cnextcn  21871  umgredg  26033  crctcshwlkn0lem5  26706  tpr2rico  29958  bj-snsetex  32951  bj-restuni  33050  poimirlem26  33435  seqpo  33543  isdrngo2  33757  pm10.55  38568  2pm13.193VD  39139