Theorem loolin 72

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. (Contributed by O'Cat, 12-Aug-2004.)

Assertion

Ref	Expression
loolin	|- (((ph -> ps) -> (ps -> ph)) -> (ps -> ph))

Proof of Theorem loolin

Step	Hyp	Ref	Expression
1		ax-1 4	. . 3 |- (ps -> (ph -> ps))
2	1	imim1i 16	. 2 |- (((ph -> ps) -> (ps -> ph)) -> (ps -> (ps -> ph)))
3	2	pm2.43d 65	1 |- (((ph -> ps) -> (ps -> ph)) -> (ps -> ph))

Syntax hints:   -> wi 3

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

Copyright terms: Public domain