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Theorem simplbi2VD 27656
Description: Virtual deduction proof of simplbi2 611. 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 ) )
3:1,?: e0_ 27581  |-  ( ( ps  /\  ch )  ->  ph )
qed:3,?: e0_ 27581  |-  ( ps  ->  ( ch  ->  ph ) )
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
pm3.26bi2VD.1  |-  ( ph  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
simplbi2VD  |-  ( ps 
->  ( ch  ->  ph )
)

Proof of Theorem simplbi2VD
StepHypRef Expression
1 pm3.26bi2VD.1 . . 3  |-  ( ph  <->  ( ps  /\  ch )
)
2 bi2 191 . . 3  |-  ( (
ph 
<->  ( ps  /\  ch ) )  ->  (
( ps  /\  ch )  ->  ph ) )
31, 2e0_ 27581 . 2  |-  ( ( ps  /\  ch )  ->  ph )
4 pm3.3 433 . 2  |-  ( ( ( ps  /\  ch )  ->  ph )  ->  ( ps  ->  ( ch  ->  ph ) ) )
53, 4e0_ 27581 1  |-  ( ps 
->  ( ch  ->  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
  Copyright terms: Public domain W3C validator