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Theorem rbaibd 876
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baibd.1  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
Assertion
Ref Expression
rbaibd  |-  ( (
ph  /\  th )  ->  ( ps  <->  ch )
)

Proof of Theorem rbaibd
StepHypRef Expression
1 baibd.1 . 2  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
2 iba 489 . . 3  |-  ( th 
->  ( ch  <->  ( ch  /\ 
th ) ) )
32bicomd 192 . 2  |-  ( th 
->  ( ( ch  /\  th )  <->  ch ) )
41, 3sylan9bb 680 1  |-  ( (
ph  /\  th )  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  qsqueeze  10544  o1lo12  12028  incexc2  12313  gexdvds  14911  fsumvma  20468
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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