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Theorem ee31 28527
Description: e31 28526 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee31.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee31.2  |-  ( ph  ->  ta )
ee31.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
ee31  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee31
StepHypRef Expression
1 ee31.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee31.2 . . . 4  |-  ( ph  ->  ta )
32a1d 22 . . 3  |-  ( ph  ->  ( ch  ->  ta ) )
43a1d 22 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
5 ee31.3 . 2  |-  ( th 
->  ( ta  ->  et ) )
61, 4, 5ee33 28284 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  trintALT  28657
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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