frege66a

Description: Swap antecedents of frege65a . Proposition 66 of Frege1879 p. 54. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege66a	$⊢ ((χ \to θ) \land (η \to ζ)) \to (((ψ \to χ) \land (τ \to η)) \to (if- (φ, ψ, τ) \to if- (φ, θ, ζ)))$

Proof

Step	Hyp	Ref	Expression
1		frege65a	$⊢ ((ψ \to χ) \land (τ \to η)) \to (((χ \to θ) \land (η \to ζ)) \to (if- (φ, ψ, τ) \to if- (φ, θ, ζ)))$
2		ax-frege8	$⊢ (((ψ \to χ) \land (τ \to η)) \to (((χ \to θ) \land (η \to ζ)) \to (if- (φ, ψ, τ) \to if- (φ, θ, ζ)))) \to (((χ \to θ) \land (η \to ζ)) \to (((ψ \to χ) \land (τ \to η)) \to (if- (φ, ψ, τ) \to if- (φ, θ, ζ))))$
3	1 2	ax-mp	$⊢ ((χ \to θ) \land (η \to ζ)) \to (((ψ \to χ) \land (τ \to η)) \to (if- (φ, ψ, τ) \to if- (φ, θ, ζ)))$

Metamath Proof Explorer

Theorem frege66a

Proof