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Theorem 3impexpbicomi 1369
Description: Deduction form of 3impexpbicom 1368. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
3impexpbicomi.1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  <->  ta )
)
Assertion
Ref Expression
3impexpbicomi  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )

Proof of Theorem 3impexpbicomi
StepHypRef Expression
1 3impexpbicomi.1 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  <->  ta )
)
21bicomd 139 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ta  <->  th )
)
323exp 1138 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
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