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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-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  f1ocnvfvrneq  5782  fcof1o  5789  isoselem  5820  isose  5821  tposss  6246  smoiso  6302  fzssp1  10066  fzosplitsnm1  10208  fzofzp1  10226  fzostep1  10236  bcm1k  10739  climuni  11300  serf0  11359  fsumparts  11477  hashiun  11485  oddprm  12258  hmeores  13785
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