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Theorem ee112 28427
Description: e112 28426 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee112.1  |-  ( ph  ->  ps )
ee112.2  |-  ( ph  ->  ch )
ee112.3  |-  ( ph  ->  ( th  ->  ta ) )
ee112.4  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee112  |-  ( ph  ->  ( th  ->  et ) )

Proof of Theorem ee112
StepHypRef Expression
1 ee112.1 . . 3  |-  ( ph  ->  ps )
21a1d 22 . 2  |-  ( ph  ->  ( th  ->  ps ) )
3 ee112.2 . . 3  |-  ( ph  ->  ch )
43a1d 22 . 2  |-  ( ph  ->  ( th  ->  ch ) )
5 ee112.3 . 2  |-  ( ph  ->  ( th  ->  ta ) )
6 ee112.4 . 2  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
72, 4, 5, 6ee222 28263 1  |-  ( ph  ->  ( th  ->  et ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
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