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Theorem bicomdd 26705
Description: Commute two sides of a biconditional in a deduction. (Contributed by Rodolfo Medina, 19-Oct-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Hypothesis
Ref Expression
bicomdd.1  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
Assertion
Ref Expression
bicomdd  |-  ( ph  ->  ( ps  ->  ( th 
<->  ch ) ) )

Proof of Theorem bicomdd
StepHypRef Expression
1 bicomdd.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
2 bicom 191 . 2  |-  ( ( ch  <->  th )  <->  ( th  <->  ch ) )
31, 2syl6ib 217 1  |-  ( ph  ->  ( ps  ->  ( th 
<->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  ibdr  26716
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
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