Metamath Proof Explorer

Theorem merlem6

Description: Step 12 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	merlem6	$⊢ χ \to (((ψ \to χ) \to φ) \to (θ \to φ))$

Proof

Step	Hyp	Ref	Expression
1		merlem4	$⊢ (ψ \to χ) \to (((ψ \to χ) \to φ) \to (θ \to φ))$
2		merlem3	$⊢ ((ψ \to χ) \to (((ψ \to χ) \to φ) \to (θ \to φ))) \to (χ \to (((ψ \to χ) \to φ) \to (θ \to φ)))$
3	1 2	ax-mp	$⊢ χ \to (((ψ \to χ) \to φ) \to (θ \to φ))$