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Theorem 3impexpbicomi 36239
Description: Inference associated with 3impexpbicom 36238. Derived automatically from 3impexpbicomiVD 36688. (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 201 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ta  <->  th )
)
323exp 1196 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ w3a 974
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  df-3an 976
This theorem is referenced by:  sbcoreleleq  36326  sbcoreleleqVD  36690
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