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Theorem ee23 1354
Description: e23 28530 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (New usage is discouraged.) TODO: decide if this is worth keeping.
Hypotheses
Ref Expression
ee23.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee23.2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
ee23.3  |-  ( ch 
->  ( ta  ->  et ) )
Assertion
Ref Expression
ee23  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )

Proof of Theorem ee23
StepHypRef Expression
1 ee23.2 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
2 ee23.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 ee23.3 . . 3  |-  ( ch 
->  ( ta  ->  et ) )
42, 3syl6 29 . 2  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
51, 4syldd 61 1  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  tz7.49  6457  rspsbc2  28297  tratrb  28299
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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