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Theorem ee1111 28278
Description: Non-virtual deduction form of e1111 28447. (Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.) The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. The completed Virtual Deduction Proof (not shown) was minimized. The minimized proof is shown.
h1::  |-  ( ph  ->  ps )
h2::  |-  ( ph  ->  ch )
h3::  |-  ( ph  ->  th )
h4::  |-  ( ph  ->  ta )
h5::  |-  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et ) ) ) )
6:1,5:  |-  ( ph  ->  ( ch  ->  ( th  ->  ( ta  ->  et ) ) ) )
7:6:  |-  ( ch  ->  ( ph  ->  ( th  ->  ( ta  ->  et ) ) ) )
8:2,7:  |-  ( ph  ->  ( ph  ->  ( th  ->  ( ta  ->  et ) ) ) )
9:8:  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
10:9:  |-  ( th  ->  ( ph  ->  ( ta  ->  et ) ) )
11:3,10:  |-  ( ph  ->  ( ph  ->  ( ta  ->  et ) ) )
12:11:  |-  ( ph  ->  ( ta  ->  et ) )
13:12:  |-  ( ta  ->  ( ph  ->  et ) )
14:4,13:  |-  ( ph  ->  ( ph  ->  et ) )
qed:14:  |-  ( ph  ->  et )
Hypotheses
Ref Expression
ee1111.1  |-  ( ph  ->  ps )
ee1111.2  |-  ( ph  ->  ch )
ee1111.3  |-  ( ph  ->  th )
ee1111.4  |-  ( ph  ->  ta )
ee1111.5  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  et ) ) ) )
Assertion
Ref Expression
ee1111  |-  ( ph  ->  et )

Proof of Theorem ee1111
StepHypRef Expression
1 ee1111.4 . 2  |-  ( ph  ->  ta )
2 ee1111.1 . . 3  |-  ( ph  ->  ps )
3 ee1111.2 . . 3  |-  ( ph  ->  ch )
4 ee1111.3 . . 3  |-  ( ph  ->  th )
5 ee1111.5 . . 3  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  et ) ) ) )
62, 3, 4, 5syl3c 57 . 2  |-  ( ph  ->  ( ta  ->  et ) )
71, 6mpd 14 1  |-  ( ph  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  e1111  28447
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator