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Metamath Proof Explorer

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	\|- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ( ps -> ph ) -> ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		jarr	\|- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ps -> ( ph -> ch ) ) )
2	1	a2d	\|- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ( ps -> ph ) -> ( ps -> ch ) ) )