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Theorem biancomd 269
Description: Commuting conjunction in a biconditional, deduction form. (Contributed by Peter Mazsa, 3-Oct-2018.)
Hypothesis
Ref Expression
biancomd.1  |-  ( ph  ->  ( ps  <->  ( th  /\  ch ) ) )
Assertion
Ref Expression
biancomd  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )

Proof of Theorem biancomd
StepHypRef Expression
1 biancomd.1 . 2  |-  ( ph  ->  ( ps  <->  ( th  /\  ch ) ) )
2 ancom 264 . 2  |-  ( ( th  /\  ch )  <->  ( ch  /\  th )
)
31, 2syl6bb 195 1  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
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:  sincosq1sgn  12923
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