Theorem frege17 43839

Description: A closed form of com3l 89. Proposition 17 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege17	⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜓 → (𝜒 → (𝜑 → 𝜃))))

Proof of Theorem frege17

Step	Hyp	Ref	Expression
1		ax-frege8 43827	. 2 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜓 → (𝜑 → (𝜒 → 𝜃))))
2		frege16 43834	. 2 ⊢ (((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜓 → (𝜑 → (𝜒 → 𝜃)))) → ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜓 → (𝜒 → (𝜑 → 𝜃)))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜓 → (𝜒 → (𝜑 → 𝜃))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 43808  ax-frege2 43809  ax-frege8 43827

This theorem is referenced by:  frege50  43872  frege78  43959