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Theorem ee121 28565
Description: e121 28733 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee121.1  |-  ( ph  ->  ps )
ee121.2  |-  ( ph  ->  ( ch  ->  th )
)
ee121.3  |-  ( ph  ->  ta )
ee121.4  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee121  |-  ( ph  ->  ( ch  ->  et ) )

Proof of Theorem ee121
StepHypRef Expression
1 ee121.1 . . 3  |-  ( ph  ->  ps )
21a1d 22 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
3 ee121.2 . 2  |-  ( ph  ->  ( ch  ->  th )
)
4 ee121.3 . . 3  |-  ( ph  ->  ta )
54a1d 22 . 2  |-  ( ph  ->  ( ch  ->  ta ) )
6 ee121.4 . 2  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
72, 3, 5, 6ee222 28562 1  |-  ( ph  ->  ( ch  ->  et ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  tratrb  28598
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