ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  4syl Unicode version

Theorem 4syl 18
Description: Inference chaining three syllogisms. The use of this theorem is marked "discouraged" because it can cause the "minimize" command to have very long run times. However, feel free to use "minimize 4syl /override" if you wish. (Contributed by BJ, 14-Jul-2018.) (New usage is discouraged.)
Hypotheses
Ref Expression
4syl.1  |-  ( ph  ->  ps )
4syl.2  |-  ( ps 
->  ch )
4syl.3  |-  ( ch 
->  th )
4syl.4  |-  ( th 
->  ta )
Assertion
Ref Expression
4syl  |-  ( ph  ->  ta )

Proof of Theorem 4syl
StepHypRef Expression
1 4syl.1 . . 3  |-  ( ph  ->  ps )
2 4syl.2 . . 3  |-  ( ps 
->  ch )
3 4syl.3 . . 3  |-  ( ch 
->  th )
41, 2, 33syl 17 . 2  |-  ( ph  ->  th )
5 4syl.4 . 2  |-  ( th 
->  ta )
64, 5syl 14 1  |-  ( ph  ->  ta )
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:  f1ocnvfvrneq  5800  fcof1o  5807  isoselem  5838  isose  5839  tposss  6266  smoiso  6322  fzssp1  10092  fzosplitsnm1  10234  fzofzp1  10252  fzostep1  10262  bcm1k  10767  climuni  11328  serf0  11387  fsumparts  11505  hashiun  11513  oddprm  12286  hmeores  14252
  Copyright terms: Public domain W3C validator