Theorem baibr 922

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 921	. 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  924  pm5.44  927  exmoeu2  2102  r19.9rmv  3552  dfopg  3817  brinxp  4743  infidc  7036  elioo5  10055  prmind2  12442  eulerthlemfi  12550  phisum  12563  pcelnn  12644  bj-charfundcALT  15745