Theorem baibr 920

Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994.)

Hypothesis

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

Assertion

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

Proof of Theorem baibr

Step	Hyp	Ref	Expression
1		baib.1	. . 3 |- ( ph <-> ( ps /\ ch ) )
2	1	baib 919	. 2 |- ( ps -> ( ph <-> ch ) )
3	2	bicomd 141	1 |- ( ps -> ( ch <-> ph ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  rbaibr  922  pm5.44  925  exmoeu2  2074  r19.9rmv  3516  dfopg  3778  brinxp  4696  elioo5  9935  prmind2  12122  eulerthlemfi  12230  pcelnn  12322  bj-charfundcALT  14646