Theorem biimpac 298

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 159	. 2 |- ( ps -> ( ph -> ch ) )
3	2	imp 124	1 |- ( ( ps /\ ph ) -> ch )

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

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  gencbvex2  2864  ordtri2or2exmidlem  4650  onsucelsucexmidlem  4653  ordsuc  4687  onsucuni2  4688  poltletr  5165  tz6.12-1  5699  nfunsn  5709  nnaordex  6763  th3qlem1  6873  ssfilem  7132  ssfilemd  7134  diffitest  7146  nqnq0pi  7755  distrlem1prl  7899  distrlem1pru  7900  eqle  8367  swrd0g  11356  flodddiv4  12626  zabsle1  15889