Full Idea
Quantifier-notation might be thus: first, render into sentences about 'properties', and use 'predicate-letters' for them; second, introduce 'variables'; third, introduce propositional logic 'connectives' and 'quantifiers'. Plus letters for 'proper names'.
Gist of Idea
Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers'
Source
E.J. Lemmon (Beginning Logic [1965], 3.1)
Book Reference
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.97