 The proof system for preminimal negation in the extended language given by the rules for distributive lattice logic together with contraposition is incomplete, and a complete proof system is obtained if \((\osim A \wedge \osim B) \vdash \osim (A \vee B)\) is added (cf. Dunn and Zhou 2005 for the language with constants \(\top\) and \(\bot\) added). The remaining fourth De Morgan law is provable in the presence of double negation elimination. The following derivation makes use of both double negation elimination and classical contraposition (cf. Restall 2000):