Theorem merlem2

Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	merlem2	⊢ ( ( ( 𝜑 → 𝜑 ) → 𝜒 ) → ( 𝜃 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		merlem1	⊢ ( ( ( ( 𝜒 → 𝜒 ) → ( ¬ 𝜑 → ¬ 𝜃 ) ) → 𝜑 ) → ( 𝜑 → 𝜑 ) )
2		meredith	⊢ ( ( ( ( ( 𝜒 → 𝜒 ) → ( ¬ 𝜑 → ¬ 𝜃 ) ) → 𝜑 ) → ( 𝜑 → 𝜑 ) ) → ( ( ( 𝜑 → 𝜑 ) → 𝜒 ) → ( 𝜃 → 𝜒 ) ) )
3	1 2	ax-mp	⊢ ( ( ( 𝜑 → 𝜑 ) → 𝜒 ) → ( 𝜃 → 𝜒 ) )