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 → 𝜓 ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) )

Proof

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