Theorem loolin

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. See loowoz for an alternate axiom. (Contributed by Mel L. O'Cat, 12-Aug-2004)

	Ref	Expression
Assertion	loolin	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜓 → 𝜑 ) ) → ( 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		jarr	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜓 → 𝜑 ) ) → ( 𝜓 → ( 𝜓 → 𝜑 ) ) )
2	1	pm2.43d	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜓 → 𝜑 ) ) → ( 𝜓 → 𝜑 ) )