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Theorem rbaibr 899
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baib.1  |-  ( ph  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
rbaibr  |-  ( ch 
->  ( ps  <->  ph ) )

Proof of Theorem rbaibr
StepHypRef Expression
1 baib.1 . . 3  |-  ( ph  <->  ( ps  /\  ch )
)
2 ancom 450 . . 3  |-  ( ( ps  /\  ch )  <->  ( ch  /\  ps )
)
31, 2bitri 249 . 2  |-  ( ph  <->  ( ch  /\  ps )
)
43baibr 897 1  |-  ( ch 
->  ( ps  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  ssunsn2  4132  cmpfi  19129  sdrgacs  29698
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