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 )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117

This theorem is used by:  gencbvex2  2870  sseq0  3565  ordtri2or2exmidlem  4675  onsucelsucexmidlem  4678  ordsuc  4712  onsucuni2  4713  poltletr  5191  tz6.12-1  5725  nfunsn  5736  nnaordex  6806  th3qlem1  6916  ssfilem  7183  ssfilemd  7185  diffitest  7197  nqnq0pi  7811  distrlem1prl  7955  distrlem1pru  7956  eqle  8423  swrd0g  11453  flodddiv4  12727  psrbagfsuppfi  15165  zabsle1  16340