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	$$⊢\left(\left(\phi \to \psi \right)\to \left(\psi \to \phi \right)\right)\to \left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		jarr	$$⊢\left(\left(\phi \to \psi \right)\to \left(\psi \to \phi \right)\right)\to \left(\psi \to \left(\psi \to \phi \right)\right)$$
2	1	pm2.43d	$$⊢\left(\left(\phi \to \psi \right)\to \left(\psi \to \phi \right)\right)\to \left(\psi \to \phi \right)$$