Theorem bi1imp 38687

Description: Importation inference similar to imp 445, except the outermost implication of the hypothesis is a biconditional. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi1imp.1	|- ( ph <-> ( ps -> ch ) )

Assertion

Ref	Expression
bi1imp	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem bi1imp

Step	Hyp	Ref	Expression
1		bi1imp.1	. . 3 |- ( ph <-> ( ps -> ch ) )
2	1	biimpi 206	. 2 |- ( ph -> ( ps -> ch ) )
3	2	imp 445	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384

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 197  df-an 386

This theorem is referenced by: (None)