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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-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  f1ocnvfvrneq  5447  fcof1o  5454  isoselem  5484  isose  5485  tposss  5889  smoiso  5945  fzssp1  9150  fzosplitsnm1  9284  fzofzp1  9302  fzostep1  9312  bcm1k  9773  climuni  10259  serif0  10316
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