Theorem imdistand 728

Description: Distribution of implication with conjunction (deduction rule). (Contributed by NM, 27-Aug-2004.)

Hypothesis

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

Assertion

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

Proof of Theorem imdistand

Step	Hyp	Ref	Expression
1		imdistand.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		imdistan 725	. 2 |- ( ( ps -> ( ch -> th ) ) <-> ( ( ps /\ ch ) -> ( ps /\ th ) ) )
3	1, 2	sylib 208	1 |- ( ph -> ( ( ps /\ ch ) -> ( ps /\ th ) ) )

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:  imdistanda  729  a2and  853  predpo  5698  unblem1  8212  cfub  9071  lbzbi  11776  poimirlem32  33441  ispridl2  33837  ispridlc  33869  lnr2i  37686  rfovcnvf1od  38298