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Theorem loolin 173
Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. For a version not using ax-3 8, see loolinALT 95. (Contributed by O'Cat, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 2-Nov-2012.)
Assertion
Ref Expression
loolin (((φψ) → (ψφ)) → (ψφ))

Proof of Theorem loolin
StepHypRef Expression
1 pm2.521 146 . 2 (¬ (φψ) → (ψφ))
2 id 19 . 2 ((ψφ) → (ψφ))
31, 2ja 153 1 (((φψ) → (ψφ)) → (ψφ))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
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