Theorem rbaibd 949

Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)

Hypothesis

Ref	Expression
baibd.1	|- ( ph -> ( ps <-> ( ch /\ th ) ) )

Assertion

Ref	Expression
rbaibd	|- ( ( ph /\ th ) -> ( ps <-> ch ) )

Proof of Theorem rbaibd

Step	Hyp	Ref	Expression
1		baibd.1	. 2 |- ( ph -> ( ps <-> ( ch /\ th ) ) )
2		iba 524	. . 3 |- ( th -> ( ch <-> ( ch /\ th ) ) )
3	2	bicomd 213	. 2 |- ( th -> ( ( ch /\ th ) <-> ch ) )
4	1, 3	sylan9bb 736	1 |- ( ( ph /\ th ) -> ( 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:  qsqueeze  12032  o1lo12  14269  incexc2  14570  gexdvds  17999  fsumvma  24938