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Theorem ee323 28269
Description: e323 28541 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee323.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee323.2  |-  ( ph  ->  ( ps  ->  ta ) )
ee323.3  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
ee323.4  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
ee323  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )

Proof of Theorem ee323
StepHypRef Expression
1 ee323.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee323.2 . . 3  |-  ( ph  ->  ( ps  ->  ta ) )
32a1dd 42 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
4 ee323.3 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
5 ee323.4 . 2  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
61, 3, 4, 5ee333 28268 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  e323  28541  trintALT  28657
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