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Theorem ee010 28457
Description: e010 28456 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee010.1  |-  ph
ee010.2  |-  ( ps 
->  ch )
ee010.3  |-  th
ee010.4  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
ee010  |-  ( ps 
->  ta )

Proof of Theorem ee010
StepHypRef Expression
1 ee010.1 . . 3  |-  ph
21a1i 10 . 2  |-  ( ps 
->  ph )
3 ee010.2 . 2  |-  ( ps 
->  ch )
4 ee010.3 . . 3  |-  th
54a1i 10 . 2  |-  ( ps 
->  th )
6 ee010.4 . 2  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
72, 3, 5, 6syl3c 57 1  |-  ( ps 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator