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Theorem 3impexpbicomi 1358
Description: Deduction form of 3impexpbicom 1357. Derived automatically from 3impexpbicomiVD 28950. (Contributed by Alan Sare, 31-Dec-2011.) (New usage is discouraged.) TODO: decide if this is worth keeping.
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 192 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ta  <->  th )
)
323exp 1150 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w3a 934
This theorem is referenced by:  sbcoreleleq  28597  sbcoreleleqVD  28951
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  df-3an 936
  Copyright terms: Public domain W3C validator