Theorem frege22 44818

Description: A closed form of com45 98. Proposition 22 of [Frege1879] p. 41. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege22	⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) → (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂))))))

Proof of Theorem frege22

Step	Hyp	Ref	Expression
1		frege16 44815	. 2 ⊢ ((𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))) → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂)))))
2		frege5 44799	. 2 ⊢ (((𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))) → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂))))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) → (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂)))))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) → (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂))))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44789  ax-frege2 44790  ax-frege8 44808

This theorem is used by:  frege23  44824