Theorem biimpac 292

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 157	. 2 |- ( ps -> ( ph -> ch ) )
3	2	imp 122	1 |- ( ( ps /\ ph ) -> ch )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  gencbvex2  2666  ordtri2or2exmidlem  4332  onsucelsucexmidlem  4335  ordsuc  4369  onsucuni2  4370  poltletr  4819  tz6.12-1  5315  nfunsn  5322  nnaordex  6266  th3qlem1  6374  ssfilem  6571  diffitest  6583  nqnq0pi  6976  distrlem1prl  7120  distrlem1pru  7121  eqle  7555  flodddiv4  11016