Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  simplbi2VD Unicode version

Theorem simplbi2VD 27995
Description: Virtual deduction proof of simplbi2 608. 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_ 27920  |-  ( ( ps  /\  ch )  ->  ph )
qed:3,?: e0_ 27920  |-  ( 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 189 . . 3  |-  ( (
ph 
<->  ( ps  /\  ch ) )  ->  (
( ps  /\  ch )  ->  ph ) )
31, 2e0_ 27920 . 2  |-  ( ( ps  /\  ch )  ->  ph )
4 pm3.3 431 . 2  |-  ( ( ( ps  /\  ch )  ->  ph )  ->  ( ps  ->  ( ch  ->  ph ) ) )
53, 4e0_ 27920 1  |-  ( ps 
->  ( ch  ->  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
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
  Copyright terms: Public domain W3C validator