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Theorem syl9 71
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Hypotheses
Ref Expression
syl9.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl9.2  |-  ( th 
->  ( ch  ->  ta ) )
Assertion
Ref Expression
syl9  |-  ( ph  ->  ( th  ->  ( ps  ->  ta ) ) )

Proof of Theorem syl9
StepHypRef Expression
1 syl9.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 syl9.2 . . 3  |-  ( th 
->  ( ch  ->  ta ) )
32a1i 9 . 2  |-  ( ph  ->  ( th  ->  ( ch  ->  ta ) ) )
41, 3syl5d 67 1  |-  ( ph  ->  ( th  ->  ( ps  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  syl9r  72  com23  77  sylan9  401  pm4.79dc  843  pclem6  1306  bilukdc  1328  sbequi  1761  reuss2  3251  reupick  3255  elres  4674  funimass4  5256  fliftfun  5467  elabgf2  10768  bj-rspgt  10774
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