Theorem rbaibr 946

Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)

Hypothesis

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

Assertion

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

Proof of Theorem rbaibr

Step	Hyp	Ref	Expression
1		iba 524	. 2 |- ( ch -> ( ps <-> ( ps /\ ch ) ) )
2		baib.1	. 2 |- ( ph <-> ( ps /\ ch ) )
3	1, 2	syl6bbr 278	1 |- ( ch -> ( ps <-> ph ) )

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:  rbaib  947  exintrbi  1818  sssseq  3621  ssunsn2  4359  cmpfi  21211  sdrgacs  37771  nanorxor  38504