Theorem biimpac 296

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

Hypothesis

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

Assertion

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

Proof of Theorem biimpac

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 |- ( ph -> ( ps <-> ch ) )
2	1	biimpcd 158	. 2 |- ( ps -> ( ph -> ch ) )
3	2	imp 123	1 |- ( ( ps /\ ph ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  gencbvex2  2736  ordtri2or2exmidlem  4449  onsucelsucexmidlem  4452  ordsuc  4486  onsucuni2  4487  poltletr  4947  tz6.12-1  5456  nfunsn  5463  nnaordex  6431  th3qlem1  6539  ssfilem  6777  diffitest  6789  nqnq0pi  7270  distrlem1prl  7414  distrlem1pru  7415  eqle  7879  flodddiv4  11667