Theorem rbaib 933

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 266	. . 3 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3	1, 2	bitri 184	. 2 |- ( ph <-> ( ch /\ ps ) )
4	3	baib 931	1 |- ( ch -> ( ph <-> ps ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  reusv1  4604  opres  5072  cores  5291  fvres  5719  fzsplit2  10455  fzsplit3  10458  ablnsg  14138  cnptoprest  15340  n0alsm  17157