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Theorem ee212 28729
Description: e212 28728 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee212.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee212.2  |-  ( ph  ->  th )
ee212.3  |-  ( ph  ->  ( ps  ->  ta ) )
ee212.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee212  |-  ( ph  ->  ( ps  ->  et ) )

Proof of Theorem ee212
StepHypRef Expression
1 ee212.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ee212.2 . . 3  |-  ( ph  ->  th )
32a1d 22 . 2  |-  ( ph  ->  ( ps  ->  th )
)
4 ee212.3 . 2  |-  ( ph  ->  ( ps  ->  ta ) )
5 ee212.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
61, 3, 4, 5ee222 28562 1  |-  ( ph  ->  ( ps  ->  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