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Theorem rbaibr 906
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)
Hypothesis
Ref Expression
baib.1  |-  ( ph  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
rbaibr  |-  ( ch 
->  ( ps  <->  ph ) )

Proof of Theorem rbaibr
StepHypRef Expression
1 iba 501 . 2  |-  ( ch 
->  ( ps  <->  ( ps  /\ 
ch ) ) )
2 baib.1 . 2  |-  ( ph  <->  ( ps  /\  ch )
)
31, 2syl6bbr 263 1  |-  ( ch 
->  ( ps  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 367
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 369
This theorem is referenced by:  rbaib  907  ssunsn2  4131  cmpfi  20201  sdrgacs  35514  nanorxor  36033
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