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Theorem rbaib 906
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 264 . . 3  |-  ( ( ps  /\  ch )  <->  ( ch  /\  ps )
)
31, 2bitri 183 . 2  |-  ( ph  <->  ( ch  /\  ps )
)
43baib 904 1  |-  ( ch 
->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  reusv1  4379  opres  4828  cores  5042  fvres  5445  fzsplit2  9837  cnptoprest  12418
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