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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 (𝜑𝜓)
4syl.2 (𝜓𝜒)
4syl.3 (𝜒𝜃)
4syl.4 (𝜃𝜏)
Assertion
Ref Expression
4syl (𝜑𝜏)

Proof of Theorem 4syl
StepHypRef Expression
1 4syl.1 . . 3 (𝜑𝜓)
2 4syl.2 . . 3 (𝜓𝜒)
3 4syl.3 . . 3 (𝜒𝜃)
41, 2, 33syl 17 . 2 (𝜑𝜃)
5 4syl.4 . 2 (𝜃𝜏)
64, 5syl 14 1 (𝜑𝜏)
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  5450  fcof1o  5457  isoselem  5487  isose  5488  tposss  5892  smoiso  5948  fzssp1  9032  fzosplitsnm1  9167  fzofzp1  9185  fzostep1  9195  bcm1k  9628  climuni  10045  serif0  10102
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