Metamath Proof Explorer

Theorem rp-misc1-frege

Description: Double-use of ax-frege2 . (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	rp-misc1-frege	$⊢ ((φ \to (ψ \to χ)) \to (φ \to ψ)) \to ((φ \to (ψ \to χ)) \to (φ \to χ))$

Step	Hyp	Ref	Expression
1		ax-frege2	$⊢ (φ \to (ψ \to χ)) \to ((φ \to ψ) \to (φ \to χ))$
2		ax-frege2	$⊢ ((φ \to (ψ \to χ)) \to ((φ \to ψ) \to (φ \to χ))) \to (((φ \to (ψ \to χ)) \to (φ \to ψ)) \to ((φ \to (ψ \to χ)) \to (φ \to χ)))$
3	1 2	ax-mp	$⊢ ((φ \to (ψ \to χ)) \to (φ \to ψ)) \to ((φ \to (ψ \to χ)) \to (φ \to χ))$