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Theorem ee002 28721
Description: e002 28720 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee002.1  |-  ph
ee002.2  |-  ps
ee002.3  |-  ( ch 
->  ( th  ->  ta ) )
ee002.4  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee002  |-  ( ch 
->  ( th  ->  et ) )

Proof of Theorem ee002
StepHypRef Expression
1 ee002.1 . . . 4  |-  ph
21a1i 10 . . 3  |-  ( th 
->  ph )
32a1i 10 . 2  |-  ( ch 
->  ( th  ->  ph )
)
4 ee002.2 . . . 4  |-  ps
54a1i 10 . . 3  |-  ( th 
->  ps )
65a1i 10 . 2  |-  ( ch 
->  ( th  ->  ps ) )
7 ee002.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
8 ee002.4 . 2  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
93, 6, 7, 8ee222 28562 1  |-  ( ch 
->  ( 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