The particle combination in the headword phrase has the sense of an emphatic denial; see LSJ s.v. mh/n II.5 and Denniston, pp. 338-9. It might be extracted from the quotation given here, though probably not, since earlier lexica (see n.4 below) do not have the quotation.
[1] See LSJ s.v. mh/n II.3 and Denniston, pp. 341-7.
[2] Adverbial; see LSJ s.v. ou)damw=s.
[3] Adverbial; see LSJ s.v. mo/nws II.2. (The entry up to this point is identical to Hesychius s.v. ou) mh/n.)
[4] This glossing as a whole collects some adverbial phrases and particle combinations that have a similar or adverse sense to that of the lemma. Identical glossing in the Synagoge, Photius' Lexicon (omicron662 Theodoridis) and Lexica Segueriana 322.15; and cf. a scholion on Plato, Laws 822C (web address 1), where the headword phrase occurs.
[5] Aelian fr. 305 Hercher (302 Domingo-Forasté).