Theorem luklem1

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 23-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	luklem1.1	⊢ ( 𝜑 → 𝜓 )
	luklem1.2	⊢ ( 𝜓 → 𝜒 )
Assertion	luklem1	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		luklem1.1	⊢ ( 𝜑 → 𝜓 )
2		luklem1.2	⊢ ( 𝜓 → 𝜒 )
3		luk-1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )
4	1 3	ax-mp	⊢ ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) )
5	2 4	ax-mp	⊢ ( 𝜑 → 𝜒 )