Metamath Proof Explorer

Theorem frege50

Description: Closed form of jaoi . Proposition 50 of Frege1879 p. 49. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege50	$⊢ (φ \to ψ) \to ((χ \to ψ) \to ((\neg φ \to χ) \to ψ))$

Step	Hyp	Ref	Expression
1		frege49	$⊢ (\neg φ \to χ) \to ((φ \to ψ) \to ((χ \to ψ) \to ψ))$
2		frege17	$⊢ ((\neg φ \to χ) \to ((φ \to ψ) \to ((χ \to ψ) \to ψ))) \to ((φ \to ψ) \to ((χ \to ψ) \to ((\neg φ \to χ) \to ψ)))$
3	1 2	ax-mp	$⊢ (φ \to ψ) \to ((χ \to ψ) \to ((\neg φ \to χ) \to ψ))$