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Theorem bj-syl66ib 33964
Description: A mixed syllogism inference derived from syl6ib 254. In addition to bj-dvelimdv1 34252, it can also shorten alexsubALTlem4 22653 (4821>4812), supsrlem 10522 (2868>2863). (Contributed by BJ, 20-Oct-2021.)
Hypotheses
Ref Expression
bj-syl66ib.1 (𝜑 → (𝜓𝜃))
bj-syl66ib.2 (𝜃𝜏)
bj-syl66ib.3 (𝜏𝜒)
Assertion
Ref Expression
bj-syl66ib (𝜑 → (𝜓𝜒))

Proof of Theorem bj-syl66ib
StepHypRef Expression
1 bj-syl66ib.1 . . 3 (𝜑 → (𝜓𝜃))
2 bj-syl66ib.2 . . 3 (𝜃𝜏)
31, 2syl6 35 . 2 (𝜑 → (𝜓𝜏))
4 bj-syl66ib.3 . 2 (𝜏𝜒)
53, 4syl6ib 254 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210
This theorem is referenced by:  bj-dvelimdv1  34252
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