Metamath Proof Explorer

Theorem merlem2

Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	merlem2	$⊢ ((φ \to φ) \to χ) \to (θ \to χ)$

Proof

Step	Hyp	Ref	Expression
1		merlem1	$⊢ (((χ \to χ) \to (\neg φ \to \neg θ)) \to φ) \to (φ \to φ)$
2		meredith	$⊢ ((((χ \to χ) \to (\neg φ \to \neg θ)) \to φ) \to (φ \to φ)) \to (((φ \to φ) \to χ) \to (θ \to χ))$
3	1 2	ax-mp	$⊢ ((φ \to φ) \to χ) \to (θ \to χ)$