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Theorem ee33 28583
Description: Non-virtual deduction form of e33 28823. (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 55 . 2  |-  ( ( ch  ->  th )  ->  ( ( ch  ->  ta )  ->  ( ch  ->  et ) ) )
51, 2, 4ee22 1352 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  truniALT  28604  onfrALTlem2  28610  ee33an  28825  ee03  28830  ee30  28834  ee31  28841  ee32  28848  trintALT  28973
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator