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Theorem ee021 27811
Description: e021 27810 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee021.1  |-  ph
ee021.2  |-  ( ps 
->  ( ch  ->  th )
)
ee021.3  |-  ( ps 
->  ta )
ee021.4  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee021  |-  ( ps 
->  ( ch  ->  et ) )

Proof of Theorem ee021
StepHypRef Expression
1 ee021.1 . . . 4  |-  ph
21a1i 10 . . 3  |-  ( ch 
->  ph )
32a1i 10 . 2  |-  ( ps 
->  ( ch  ->  ph )
)
4 ee021.2 . 2  |-  ( ps 
->  ( ch  ->  th )
)
5 ee021.3 . . 3  |-  ( ps 
->  ta )
65a1d 22 . 2  |-  ( ps 
->  ( ch  ->  ta ) )
7 ee021.4 . 2  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
83, 4, 6, 7ee222 27636 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