Theorem loowoz 73

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

Assertion

Ref	Expression
loowoz	|- (((ph -> ps) -> (ph -> ch)) -> ((ps -> ph) -> (ps -> ch)))

Proof of Theorem loowoz

Step	Hyp	Ref	Expression
1		ax-1 4	. . 3 |- (ps -> (ph -> ps))
2	1	imim1i 16	. 2 |- (((ph -> ps) -> (ph -> ch)) -> (ps -> (ph -> ch)))
3	2	a2d 13	1 |- (((ph -> ps) -> (ph -> ch)) -> ((ps -> ph) -> (ps -> ch)))

Syntax hints:   -> wi 3

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

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