Metamath Proof Explorer

Theorem luklem5

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	luklem5	$⊢ φ \to (ψ \to φ)$

Proof

Step	Hyp	Ref	Expression
1		luklem3	$⊢ φ \to (((\neg φ \to φ) \to φ) \to (ψ \to φ))$
2		luklem4	$⊢ (((\neg φ \to φ) \to φ) \to (ψ \to φ)) \to (ψ \to φ)$
3	1 2	luklem1	$⊢ φ \to (ψ \to φ)$