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Theorem prtlem60 25869
Description: Lemma for prter3 25916. (Contributed by Rodolfo Medina, 9-Oct-2010.)
Hypotheses
Ref Expression
prtlem60.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
prtlem60.2  |-  ( ps 
->  ( th  ->  ta ) )
Assertion
Ref Expression
prtlem60  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )

Proof of Theorem prtlem60
StepHypRef Expression
1 prtlem60.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 prtlem60.2 . . 3  |-  ( ps 
->  ( th  ->  ta ) )
32a1i 12 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
41, 3syldd 63 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10
  Copyright terms: Public domain W3C validator