Theorem frege17 40160

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 40148	. 2 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜓 → (𝜑 → (𝜒 → 𝜃))))
2		frege16 40155	. 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 40129  ax-frege2 40130  ax-frege8 40148

This theorem is referenced by:  frege50  40193  frege78  40280