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Theorem ee32an 28971
Description: e33an 28945 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee32an.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee32an.2  |-  ( ph  ->  ( ps  ->  ta ) )
ee32an.3  |-  ( ( th  /\  ta )  ->  et )
Assertion
Ref Expression
ee32an  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee32an
StepHypRef Expression
1 ee32an.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee32an.2 . . 3  |-  ( ph  ->  ( ps  ->  ta ) )
32a1dd 45 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
4 ee32an.3 . 2  |-  ( ( th  /\  ta )  ->  et )
51, 3, 4ee33an 28946 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362
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