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Theorem ee123 28852
Description: e123 28851 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee123.1  |-  ( ph  ->  ps )
ee123.2  |-  ( ph  ->  ( ch  ->  th )
)
ee123.3  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
ee123.4  |-  ( ps 
->  ( th  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
ee123  |-  ( ph  ->  ( ch  ->  ( ta  ->  ze ) ) )

Proof of Theorem ee123
StepHypRef Expression
1 ee123.1 . . . 4  |-  ( ph  ->  ps )
21a1d 22 . . 3  |-  ( ph  ->  ( ta  ->  ps ) )
32a1d 22 . 2  |-  ( ph  ->  ( ch  ->  ( ta  ->  ps ) ) )
4 ee123.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
54a1dd 42 . 2  |-  ( ph  ->  ( ch  ->  ( ta  ->  th ) ) )
6 ee123.3 . 2  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
7 ee123.4 . 2  |-  ( ps 
->  ( th  ->  ( et  ->  ze ) ) )
83, 5, 6, 7ee333 28567 1  |-  ( ph  ->  ( ch  ->  ( ta  ->  ze ) ) )
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  df-3an 936
  Copyright terms: Public domain W3C validator