Theorem biimparc 473

Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)

Hypothesis

Ref	Expression
biimpa.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
biimparc	|- ((ch /\ ph) -> ps)

Proof of Theorem biimparc

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 |- (ph -> (ps <-> ch))
2	1	biimprcd 216	. 2 |- (ch -> (ph -> ps))
3	2	imp 418	1 |- ((ch /\ ph) -> ps)

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

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

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

This theorem is referenced by:  biantr  897  difprsnss  3847  fun11iun  5306  eqfnfv2  5394  fmpt  5693