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Theorem ee33 28667
Description: Non-virtual deduction form of e33 28908. (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  ->  ( ch  ->  th ) ) )
h2::  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
h3::  |-  ( th  ->  ( ta  ->  et ) )
4:1,3:  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  et ) ) ) )
5:4:  |-  ( ta  ->  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) ) )
6:2,5:  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) ) ) ) )
7:6:  |-  ( ps  ->  ( ch  ->  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) ) ) )
8:7:  |-  ( ch  ->  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) ) )
qed:8:  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Hypotheses
Ref Expression
ee33.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee33.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
ee33.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
ee33  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee33
StepHypRef Expression
1 ee33.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee33.2 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
3 ee33.3 . . 3  |-  ( th 
->  ( ta  ->  et ) )
43imim3i 58 . 2  |-  ( ( ch  ->  th )  ->  ( ( ch  ->  ta )  ->  ( ch  ->  et ) ) )
51, 2, 4ee22 1372 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  truniALT  28688  onfrALTlem2  28694  ee33an  28910  ee03  28915  ee30  28919  ee31  28926  ee32  28933  trintALT  29055
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator