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  2893  difprsnss  3731  elpw2g  4157  elon2  4377  ideqg  4779  elrnmpt1s  4878  elrnmptg  4880  fun11iun  5483  eqfnfv2  5615  fmpt  5667  elunirn  5767  spc2ed  6234  tposfo2  6268  tposf12  6270  dom2lem  6772  enfii  6874  ac6sfi  6898  ltexprlemm  7599  elreal2  7829  fihasheqf1oi  10767  fprod2dlemstep  11630  bastop2  13587