Theorem frege22

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

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

Proof

Step	Hyp	Ref	Expression
1		frege16	⊢ ( ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) → ( 𝜓 → ( 𝜒 → ( 𝜏 → ( 𝜃 → 𝜂 ) ) ) ) )
2		frege5	⊢ ( ( ( 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	⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) → ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜏 → ( 𝜃 → 𝜂 ) ) ) ) ) )