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Theorem syl10 1394
Description: A nested syllogism inference. (Contributed by Alan Sare, 17-Jul-2011.)
Hypotheses
Ref Expression
syl10.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl10.2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
syl10.3  |-  ( ch 
->  ( ta  ->  et ) )
Assertion
Ref Expression
syl10  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )

Proof of Theorem syl10
StepHypRef Expression
1 syl10.2 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
2 syl10.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 syl10.3 . . 3  |-  ( ch 
->  ( ta  ->  et ) )
42, 3syl6 33 . 2  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
51, 4syldd 67 1  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator