ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl9 Unicode version

Theorem syl9 72
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 68 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  73  com23  78  sylan9  404  pm4.79dc  853  pclem6  1320  bilukdc  1342  sbequi  1778  reuss2  3303  reupick  3307  elres  4791  funimass4  5404  fliftfun  5629  elabgf2  12568  bj-rspgt  12574
  Copyright terms: Public domain W3C validator