Theorem rbaibd 833

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 284	. . 3 |- ( th -> ( ch <-> ( ch /\ th ) ) )
3	2	bicomd 129	. 2 |- ( th -> ( ( ch /\ th ) <-> ch ) )
4	1, 3	sylan9bb 435	1 |- ( ( ph /\ th ) -> ( ps <-> ch ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)