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Theorem ee03 28830
Description: e03 28829 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee03.1  |-  ph
ee03.2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
ee03.3  |-  ( ph  ->  ( ta  ->  et ) )
Assertion
Ref Expression
ee03  |-  ( ps 
->  ( ch  ->  ( th  ->  et ) ) )

Proof of Theorem ee03
StepHypRef Expression
1 ee03.1 . . . . 5  |-  ph
21a1i 10 . . . 4  |-  ( ps 
->  ph )
32a1d 22 . . 3  |-  ( ps 
->  ( ch  ->  ph )
)
43a1dd 42 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ph ) ) )
5 ee03.2 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
6 ee03.3 . 2  |-  ( ph  ->  ( ta  ->  et ) )
74, 5, 6ee33 28583 1  |-  ( ps 
->  ( ch  ->  ( th  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  ee03an  28832  suctrALT2  28929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator