Metamath Proof Explorer

Theorem frege58acor

Description: Lemma for frege59a . (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege58acor	$⊢ ((ψ \to χ) \land (θ \to τ)) \to (if- (φ, ψ, θ) \to if- (φ, χ, τ))$

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