Metamath Proof Explorer

Theorem frege61a

Description: Lemma for frege65a . Proposition 61 of Frege1879 p. 52. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege61a	$⊢ (if- (φ, ψ, χ) \to θ) \to ((ψ \land χ) \to θ)$

Step	Hyp	Ref	Expression
1		ax-frege58a	$⊢ (ψ \land χ) \to if- (φ, ψ, χ)$
2		frege9	$⊢ ((ψ \land χ) \to if- (φ, ψ, χ)) \to ((if- (φ, ψ, χ) \to θ) \to ((ψ \land χ) \to θ))$
3	1 2	ax-mp	$⊢ (if- (φ, ψ, χ) \to θ) \to ((ψ \land χ) \to θ)$