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Theorem ee022 28414
Description: e022 28413 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee022.1  |-  ph
ee022.2  |-  ( ps 
->  ( ch  ->  th )
)
ee022.3  |-  ( ps 
->  ( ch  ->  ta ) )
ee022.4  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee022  |-  ( ps 
->  ( ch  ->  et ) )

Proof of Theorem ee022
StepHypRef Expression
1 ee022.1 . . . 4  |-  ph
21a1i 10 . . 3  |-  ( ch 
->  ph )
32a1i 10 . 2  |-  ( ps 
->  ( ch  ->  ph )
)
4 ee022.2 . 2  |-  ( ps 
->  ( ch  ->  th )
)
5 ee022.3 . 2  |-  ( ps 
->  ( ch  ->  ta ) )
6 ee022.4 . 2  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
73, 4, 5, 6ee222 28263 1  |-  ( ps 
->  ( ch  ->  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