Theorem bi2imp 38688

Description: Importation inference similar to imp 445, except both implications of the hypothesis are biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi2imp.1	|- ( ph <-> ( ps <-> ch ) )

Assertion

Ref	Expression
bi2imp	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem bi2imp

Step	Hyp	Ref	Expression
1		bi2imp.1	. . 3 |- ( ph <-> ( ps <-> ch ) )
2	1	biimpi 206	. 2 |- ( ph -> ( ps <-> ch ) )
3	2	biimpa 501	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)