Metamath Proof Explorer

Theorem frege62a

Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara when the minor premise has a particular context. Proposition 62 of Frege1879 p. 52. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege62a	$⊢ if- (φ, ψ, θ) \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ))$

Proof

Step	Hyp	Ref	Expression
1		frege58acor	$⊢ ((ψ \to χ) \land (θ \to τ)) \to (if- (φ, ψ, θ) \to if- (φ, χ, τ))$
2		ax-frege8	$⊢ (((ψ \to χ) \land (θ \to τ)) \to (if- (φ, ψ, θ) \to if- (φ, χ, τ))) \to (if- (φ, ψ, θ) \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ)))$
3	1 2	ax-mp	$⊢ if- (φ, ψ, θ) \to (((ψ \to χ) \land (θ \to τ)) \to if- (φ, χ, τ))$