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Theorem ee13 28564
Description: e13 28837 without virtual deduction connectives. Special theorem needed for Alan Sare's virtual deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee13.1  |-  ( ph  ->  ps )
ee13.2  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
ee13.3  |-  ( ps 
->  ( ta  ->  et ) )
Assertion
Ref Expression
ee13  |-  ( ph  ->  ( ch  ->  ( th  ->  et ) ) )

Proof of Theorem ee13
StepHypRef Expression
1 ee13.2 . 2  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
2 ee13.1 . . 3  |-  ( ph  ->  ps )
3 ee13.3 . . 3  |-  ( ps 
->  ( ta  ->  et ) )
42, 3syl 15 . 2  |-  ( ph  ->  ( ta  ->  et ) )
51, 4syl6d 64 1  |-  ( ph  ->  ( ch  ->  ( th  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  sbcim2g  28601  ee13an  28839
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator