ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syld3an1 Unicode version

Theorem syld3an1 1216
Description: A syllogism inference. (Contributed by NM, 7-Jul-2008.)
Hypotheses
Ref Expression
syld3an1.1  |-  ( ( ch  /\  ps  /\  th )  ->  ph )
syld3an1.2  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Assertion
Ref Expression
syld3an1  |-  ( ( ch  /\  ps  /\  th )  ->  ta )

Proof of Theorem syld3an1
StepHypRef Expression
1 syld3an1.1 . . . 4  |-  ( ( ch  /\  ps  /\  th )  ->  ph )
213com13 1144 . . 3  |-  ( ( th  /\  ps  /\  ch )  ->  ph )
3 syld3an1.2 . . . 4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
433com13 1144 . . 3  |-  ( ( th  /\  ps  /\  ph )  ->  ta )
52, 4syld3an3 1215 . 2  |-  ( ( th  /\  ps  /\  ch )  ->  ta )
653com13 1144 1  |-  ( ( ch  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  tfrcllembacc  6024  npncan  7448  nnpcan  7450  ppncan  7469  muldivdirap  7914  div2negap  7942  ltmuldiv  8071  mulqmod0  9464
  Copyright terms: Public domain W3C validator