Metamath Proof Explorer

Theorem luklem8

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	luklem8	$⊢ (φ \to ψ) \to ((χ \to φ) \to (χ \to ψ))$

Proof

Step	Hyp	Ref	Expression
1		luk-1	$⊢ (χ \to φ) \to ((φ \to ψ) \to (χ \to ψ))$
2		luklem7	$⊢ ((χ \to φ) \to ((φ \to ψ) \to (χ \to ψ))) \to ((φ \to ψ) \to ((χ \to φ) \to (χ \to ψ)))$
3	1 2	ax-mp	$⊢ (φ \to ψ) \to ((χ \to φ) \to (χ \to ψ))$