Theorem biimparc 299

Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)

Hypothesis

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

Assertion

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

Proof of Theorem biimparc

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 |- ( ph -> ( ps <-> ch ) )
2	1	biimprcd 160	. 2 |- ( ch -> ( ph -> ps ) )
3	2	imp 124	1 |- ( ( ch /\ ph ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

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 depends on definitions:  df-bi 117

This theorem is referenced by:  biantr  952  elrab3t  2892  difprsnss  3730  elpw2g  4156  elon2  4376  ideqg  4778  elrnmpt1s  4877  elrnmptg  4879  fun11iun  5482  eqfnfv2  5614  fmpt  5666  elunirn  5766  spc2ed  6233  tposfo2  6267  tposf12  6269  dom2lem  6771  enfii  6873  ac6sfi  6897  ltexprlemm  7598  elreal2  7828  fihasheqf1oi  10766  fprod2dlemstep  11629  bastop2  13554