Theorem loowoz

Description: An alternate for the Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz loolin , due to Barbara Wozniakowska, Reports on Mathematical Logic 10, 129-137 (1978). (Contributed by Mel L. O'Cat, 8-Aug-2004)

	Ref	Expression
Assertion	loowoz	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\to \left(\left(\psi \to \phi \right)\to \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		jarr	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$
2	1	a2d	$$⊢\left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\to \left(\left(\psi \to \phi \right)\to \left(\psi \to \chi \right)\right)$$