Theorem rbaib 864

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

Hypothesis

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

Assertion

Ref	Expression
rbaib	|- ( ch -> ( ph <-> ps ) )

Proof of Theorem rbaib

Step	Hyp	Ref	Expression
1		baib.1	. . 3 |- ( ph <-> ( ps /\ ch ) )
2		ancom 262	. . 3 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3	1, 2	bitri 182	. 2 |- ( ph <-> ( ch /\ ps ) )
4	3	baib 862	1 |- ( ch -> ( ph <-> ps ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  reusv1  4216  opres  4649  cores  4854  fvres  5230  fzsplit2  9145