Theorem biimpac 472

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 215	. 2 |- (ps -> (ph -> ch))
3	2	imp 418	1 |- ((ps /\ ph) -> ch)

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  gencbvex2  2902  2reu5  3044  vfinspsslem1  4550  phi11lem1  4595  0cnelphi  4597  ideqg2  4869  nfunsn  5353  leltctr  6212  tlecg  6230  nchoicelem3  6291