Theorem frege6

Description: A closed form of imim2d which is a deduction adding nested antecedents. Proposition 6 of Frege1879 p. 33. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege6	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege5	⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) )
2		frege5	⊢ ( ( ( 𝜓 → 𝜒 ) → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) ) → ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) ) )