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Theorem looinv 185
Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 412, 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  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( ( ps  ->  ph )  ->  ph ) )

Proof of Theorem looinv
StepHypRef Expression
1 imim1 79 . 2  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( ( ps  ->  ph )  ->  ( ( ph  ->  ps )  ->  ph ) ) )
2 peirce 184 . 2  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )
31, 2syl6 34 1  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( ( ps  ->  ph )  ->  ph ) )
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  1615  bj-looinvi  30926
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