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Theorem frege23 36938
Description: Syllogism followed by rotation of three antecedents. Proposition 23 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege23 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜏𝜑) → (𝜓 → (𝜒 → (𝜏𝜃)))))

Proof of Theorem frege23
StepHypRef Expression
1 frege18 36931 . 2 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜏𝜑) → (𝜓 → (𝜏 → (𝜒𝜃)))))
2 frege22 36932 . 2 (((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜏𝜑) → (𝜓 → (𝜏 → (𝜒𝜃))))) → ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜏𝜑) → (𝜓 → (𝜒 → (𝜏𝜃))))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜏𝜑) → (𝜓 → (𝜒 → (𝜏𝜃)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36903  ax-frege2 36904  ax-frege8 36922
This theorem is referenced by:  frege48  36965
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