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Theorem looinv 174
Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 400, we can see that this essentially expresses "disjunction commutes." Theorem *2.69 of [WhiteheadRussell] p. 108. (Contributed by NM, 12-Aug-2004.)
Assertion
Ref Expression
looinv (((φψ) → ψ) → ((ψφ) → φ))

Proof of Theorem looinv
StepHypRef Expression
1 imim1 70 . 2 (((φψ) → ψ) → ((ψφ) → ((φψ) → φ)))
2 peirce 172 . 2 (((φψ) → φ) → φ)
31, 2syl6 29 1 (((φψ) → ψ) → ((ψφ) → φ))
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:  merco2  1501
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