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Theorem 3impexpbicomiVD 28679
Description: Virtual deduction proof of 3impexpbicomi 1374. 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_ 28593  |-  ( 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 1373 . . 3  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  ( th 
<->  ta ) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) ) )
32biimpi 187 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  ( th 
<->  ta ) )  -> 
( ph  ->  ( ps 
->  ( ch  ->  ( ta 
<->  th ) ) ) ) )
41, 3e0_ 28593 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  <->  th )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ w3a 936
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator