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  2647  ordtri2or2exmidlem  4277  onsucelsucexmidlem  4280  ordsuc  4314  onsucuni2  4315  poltletr  4755  tz6.12-1  5232  nfunsn  5239  nnaordex  6166  th3qlem1  6274  ssfilem  6410  diffitest  6421  nqnq0pi  6690  distrlem1prl  6834  distrlem1pru  6835  eqle  7269  flodddiv4  10478