Metamath Proof Explorer

Theorem frege19

Description: A closed form of syl6 . Proposition 19 of Frege1879 p. 39. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege19	$⊢ (φ \to (ψ \to χ)) \to ((χ \to θ) \to (φ \to (ψ \to θ)))$

Step	Hyp	Ref	Expression
1		frege9	$⊢ (ψ \to χ) \to ((χ \to θ) \to (ψ \to θ))$
2		frege18	$⊢ ((ψ \to χ) \to ((χ \to θ) \to (ψ \to θ))) \to ((φ \to (ψ \to χ)) \to ((χ \to θ) \to (φ \to (ψ \to θ))))$
3	1 2	ax-mp	$⊢ (φ \to (ψ \to χ)) \to ((χ \to θ) \to (φ \to (ψ \to θ)))$