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Theorem rbaib 864
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
StepHypRef Expression
1 baib.1 . . 3  |-  ( ph  <->  ( ps  /\  ch )
)
2 ancom 262 . . 3  |-  ( ( ps  /\  ch )  <->  ( ch  /\  ps )
)
31, 2bitri 182 . 2  |-  ( ph  <->  ( ch  /\  ps )
)
43baib 862 1  |-  ( ch 
->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  reusv1  4216  opres  4649  cores  4854  fvres  5230  fzsplit2  9145
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