Metamath Proof Explorer


Theorem looinv

Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 , 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 . (Contributed by NM, 12-Aug-2004)

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

Proof

Step Hyp Ref Expression
1 imim1
 |-  ( ( ( ph -> ps ) -> ps ) -> ( ( ps -> ph ) -> ( ( ph -> ps ) -> ph ) ) )
2 peirce
 |-  ( ( ( ph -> ps ) -> ph ) -> ph )
3 1 2 syl6
 |-  ( ( ( ph -> ps ) -> ps ) -> ( ( ps -> ph ) -> ph ) )