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Theorem ee012 28440
Description: e012 28439 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee012.1  |-  ph
ee012.2  |-  ( ps 
->  ch )
ee012.3  |-  ( ps 
->  ( th  ->  ta ) )
ee012.4  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee012  |-  ( ps 
->  ( th  ->  et ) )

Proof of Theorem ee012
StepHypRef Expression
1 ee012.1 . . . 4  |-  ph
21a1i 10 . . 3  |-  ( th 
->  ph )
32a1i 10 . 2  |-  ( ps 
->  ( th  ->  ph )
)
4 ee012.2 . . 3  |-  ( ps 
->  ch )
54a1d 22 . 2  |-  ( ps 
->  ( th  ->  ch ) )
6 ee012.3 . 2  |-  ( ps 
->  ( th  ->  ta ) )
7 ee012.4 . 2  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
83, 5, 6, 7ee222 28263 1  |-  ( ps 
->  ( th  ->  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