Metamath Proof Explorer


Theorem loolin

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. See loowoz for an alternate axiom. (Contributed by Mel L. O'Cat, 12-Aug-2004)

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

Proof

Step Hyp Ref Expression
1 jarr
 |-  ( ( ( ph -> ps ) -> ( ps -> ph ) ) -> ( ps -> ( ps -> ph ) ) )
2 1 pm2.43d
 |-  ( ( ( ph -> ps ) -> ( ps -> ph ) ) -> ( ps -> ph ) )