Theorem frege23 43816

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 → (𝜒 → 𝜃))) → ((𝜏 → 𝜑) → (𝜓 → (𝜒 → (𝜏 → 𝜃)))))

Proof of Theorem frege23

Step	Hyp	Ref	Expression
1		frege18 43809	. 2 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜏 → 𝜑) → (𝜓 → (𝜏 → (𝜒 → 𝜃)))))
2		frege22 43810	. 2 ⊢ (((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜏 → 𝜑) → (𝜓 → (𝜏 → (𝜒 → 𝜃))))) → ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜏 → 𝜑) → (𝜓 → (𝜒 → (𝜏 → 𝜃))))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜏 → 𝜑) → (𝜓 → (𝜒 → (𝜏 → 𝜃)))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 43781  ax-frege2 43782  ax-frege8 43800

This theorem is referenced by:  frege48  43843