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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  5561  fcof1o  5568  isoselem  5599  isose  5600  tposss  6011  smoiso  6067  fzssp1  9481  fzosplitsnm1  9620  fzofzp1  9638  fzostep1  9648  bcm1k  10168  climuni  10681  serf0  10741  fsumparts  10864  hashiun  10872
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