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  2777  ordtri2or2exmidlem  4508  onsucelsucexmidlem  4511  ordsuc  4545  onsucuni2  4546  poltletr  5009  tz6.12-1  5521  nfunsn  5528  nnaordex  6504  th3qlem1  6612  ssfilem  6850  diffitest  6862  nqnq0pi  7389  distrlem1prl  7533  distrlem1pru  7534  eqle  8000  flodddiv4  11882  zabsle1  13655