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Theorem looinv 194
Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 426, we can see that this essentially expresses "disjunction commutes." Theorem *2.69 of [WhiteheadRussell] p. 108. It is a special instance of the axiom "Roll", see peirceroll 85. (Contributed by NM, 12-Aug-2004.)
Assertion
Ref Expression
looinv (((𝜑𝜓) → 𝜓) → ((𝜓𝜑) → 𝜑))

Proof of Theorem looinv
StepHypRef Expression
1 imim1 83 . 2 (((𝜑𝜓) → 𝜓) → ((𝜓𝜑) → ((𝜑𝜓) → 𝜑)))
2 peirce 193 . 2 (((𝜑𝜓) → 𝜑) → 𝜑)
31, 2syl6 35 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  1774  bj-looinvi  32781
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