Theorem baib 926

Description: Move conjunction outside of biconditional. (Contributed by NM, 13-May-1999.)

Hypothesis

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

Assertion

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

Proof of Theorem baib

Step	Hyp	Ref	Expression
1		baib.1	. 2 |- ( ph <-> ( ps /\ ch ) )
2		ibar 301	. 2 |- ( ps -> ( ch <-> ( ps /\ ch ) ) )
3	1, 2	bitr4id 199	1 |- ( ps -> ( ph <-> ch ) )

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:  baibr  927  rbaib  928  ceqsrexbv  2937  elrab3  2963  rabsn  3736  elrint2  3969  frind  4449  fnres  5449  f1ompt  5798  fliftfun  5937  ovid  6138  brdifun  6729  xpcomco  7010  isacnm  7418  ltexprlemdisj  7826  xrlenlt  8244  reapval  8756  znnnlt1  9527  difrp  9927  elfz  10249  fzolb2  10390  elfzo3  10399  fzouzsplit  10416  bitsval2  12523  rpexp  12743  isghm3  13849  isabl2  13899  dfrhm2  14187  bastop1  14826  cnntr  14968  lmres  14991  tx1cn  15012  tx2cn  15013  xmetec  15180  lgsabs1  15787