Metamath Proof Explorer

Theorem luklem3

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	luklem3	$⊢ φ \to (((\neg φ \to ψ) \to χ) \to (θ \to χ))$

Proof

Step	Hyp	Ref	Expression
1		luk-3	$⊢ φ \to (\neg φ \to \neg θ)$
2		luklem2	$⊢ (\neg φ \to \neg θ) \to (((\neg φ \to ψ) \to χ) \to (θ \to χ))$
3	1 2	luklem1	$⊢ φ \to (((\neg φ \to ψ) \to χ) \to (θ \to χ))$