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	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) → ( ( 𝜓 → 𝜑 ) → ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		jarr	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) )
2	1	a2d	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) → ( ( 𝜓 → 𝜑 ) → ( 𝜓 → 𝜒 ) ) )