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Theorem ee03an 28518
Description: Conjunction form of ee03 28516. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee03an.1  |-  ph
ee03an.2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
ee03an.3  |-  ( (
ph  /\  ta )  ->  et )
Assertion
Ref Expression
ee03an  |-  ( ps 
->  ( ch  ->  ( th  ->  et ) ) )

Proof of Theorem ee03an
StepHypRef Expression
1 ee03an.1 . 2  |-  ph
2 ee03an.2 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
3 ee03an.3 . . 3  |-  ( (
ph  /\  ta )  ->  et )
43ex 423 . 2  |-  ( ph  ->  ( ta  ->  et ) )
51, 2, 4ee03 28516 1  |-  ( ps 
->  ( ch  ->  ( th  ->  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