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Theorem 3impexpbicomiVD 28634
Description: Virtual deduction proof of 3impexpbicomi 1358. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.
h1::  |-  ( ( ph  /\  ps  /\  ch )  ->  ( th  <->  ta ) )
qed:1,?: e0_ 28547  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th ) ) ) )
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
3impexpbicomiVD.1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  <->  ta )
)
Assertion
Ref Expression
3impexpbicomiVD  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )

Proof of Theorem 3impexpbicomiVD
StepHypRef Expression
1 3impexpbicomiVD.1 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  <->  ta )
)
2 3impexpbicom 1357 . . 3  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  ( th 
<->  ta ) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) ) )
32biimpi 186 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  ( th 
<->  ta ) )  -> 
( ph  ->  ( ps 
->  ( ch  ->  ( ta 
<->  th ) ) ) ) )
41, 3e0_ 28547 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w3a 934
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