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Theorem ee31an 28529
Description: e31an 28528 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee31an.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee31an.2  |-  ( ph  ->  ta )
ee31an.3  |-  ( ( th  /\  ta )  ->  et )
Assertion
Ref Expression
ee31an  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee31an
StepHypRef Expression
1 ee31an.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee31an.2 . . . 4  |-  ( ph  ->  ta )
32a1d 22 . . 3  |-  ( ph  ->  ( ch  ->  ta ) )
43a1d 22 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
5 ee31an.3 . 2  |-  ( ( th  /\  ta )  ->  et )
61, 4, 5ee33an 28511 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator