Metamath Proof Explorer

Theorem frege51

Description: Compare with jaod . Proposition 51 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege51	$⊢ (φ \to (ψ \to χ)) \to ((θ \to χ) \to (φ \to ((\neg ψ \to θ) \to χ)))$

Step	Hyp	Ref	Expression
1		frege50	$⊢ (ψ \to χ) \to ((θ \to χ) \to ((\neg ψ \to θ) \to χ))$
2		frege18	$⊢ ((ψ \to χ) \to ((θ \to χ) \to ((\neg ψ \to θ) \to χ))) \to ((φ \to (ψ \to χ)) \to ((θ \to χ) \to (φ \to ((\neg ψ \to θ) \to χ))))$
3	1 2	ax-mp	$⊢ (φ \to (ψ \to χ)) \to ((θ \to χ) \to (φ \to ((\neg ψ \to θ) \to χ)))$