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Theorem ee32 28848
Description: e32 28847 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee32.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee32.2  |-  ( ph  ->  ( ps  ->  ta ) )
ee32.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
ee32  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee32
StepHypRef Expression
1 ee32.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee32.2 . . 3  |-  ( ph  ->  ( ps  ->  ta ) )
32a1dd 42 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
4 ee32.3 . 2  |-  ( th 
->  ( ta  ->  et ) )
51, 3, 4ee33 28583 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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