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Theorem ee333 28268
Description: e333 28508 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee333.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee333.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
ee333.3  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
ee333.4  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
ee333  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )

Proof of Theorem ee333
StepHypRef Expression
1 ee333.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
213imp 1145 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
3 ee333.2 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
433imp 1145 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ta )
5 ee333.3 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
653imp 1145 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  et )
7 ee333.4 . . 3  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
82, 4, 6, 7syl3c 57 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ze )
983exp 1150 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem is referenced by:  ee323  28269  ee123  28538
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