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Theorem ee120 28436
Description: Virtual deduction rule e120 28435 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee120.1  |-  ( ph  ->  ps )
ee120.2  |-  ( ph  ->  ( ch  ->  th )
)
ee120.3  |-  ta
ee120.4  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee120  |-  ( ph  ->  ( ch  ->  et ) )

Proof of Theorem ee120
StepHypRef Expression
1 ee120.1 . . 3  |-  ( ph  ->  ps )
21a1d 22 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
3 ee120.2 . 2  |-  ( ph  ->  ( ch  ->  th )
)
4 ee120.3 . . . 4  |-  ta
54a1i 10 . . 3  |-  ( ch 
->  ta )
65a1i 10 . 2  |-  ( ph  ->  ( ch  ->  ta ) )
7 ee120.4 . 2  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
82, 3, 6, 7ee222 28263 1  |-  ( ph  ->  ( ch  ->  et ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  pwtrrOLD  28601
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