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Theorem syl11 31
Description: A syllogism inference. Commuted form of an instance of syl 14. (Contributed by BJ, 25-Oct-2021.)
Hypotheses
Ref Expression
syl11.1 (𝜑 → (𝜓𝜒))
syl11.2 (𝜃𝜑)
Assertion
Ref Expression
syl11 (𝜓 → (𝜃𝜒))

Proof of Theorem syl11
StepHypRef Expression
1 syl11.2 . . 3 (𝜃𝜑)
2 syl11.1 . . 3 (𝜑 → (𝜓𝜒))
31, 2syl 14 . 2 (𝜃 → (𝜓𝜒))
43com12 30 1 (𝜓 → (𝜃𝜒))
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:  alzdvds  10166
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