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  4654  onsucelsucexmidlem  4657  ordsuc  4691  onsucuni2  4692  poltletr  5169  tz6.12-1  5703  nfunsn  5713  nnaordex  6775  th3qlem1  6885  ssfilem  7144  ssfilemd  7146  diffitest  7158  nqnq0pi  7770  distrlem1prl  7914  distrlem1pru  7915  eqle  8382  swrd0g  11381  flodddiv4  12652  zabsle1  16003