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Theorem ee33 36921
Description: Non-virtual deduction form of e33 37160. (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 L. 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 61 . 2  |-  ( ( ch  ->  th )  ->  ( ( ch  ->  ta )  ->  ( ch  ->  et ) ) )
51, 2, 4syl6c 66 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  truniALT  36945  onfrALTlem2  36955  ee33an  37162  ee03  37167  ee30  37171  ee31  37178  ee32  37185  trintALT  37317
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