Metamath Proof Explorer

Theorem frege63a

Description: Proposition 63 of Frege1879 p. 52. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege63a	$⊢ if- (φ, ψ, θ) \to (η \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ)))$

Step	Hyp	Ref	Expression
1		frege62a	$⊢ if- (φ, ψ, θ) \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ))$
2		frege24	$⊢ (if- (φ, ψ, θ) \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ))) \to (if- (φ, ψ, θ) \to (η \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ))))$
3	1 2	ax-mp	$⊢ if- (φ, ψ, θ) \to (η \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ)))$