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Theorem ee33an 28511
Description: e33an 28510 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee33an.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee33an.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
ee33an.3  |-  ( ( th  /\  ta )  ->  et )
Assertion
Ref Expression
ee33an  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee33an
StepHypRef Expression
1 ee33an.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee33an.2 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
3 ee33an.3 . . 3  |-  ( ( th  /\  ta )  ->  et )
43ex 423 . 2  |-  ( th 
->  ( ta  ->  et ) )
51, 2, 4ee33 28284 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  ee31an  28529  ee23an  28532  ee32an  28536
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