Definition 31: A class x is called a set if there exists a class y with x \in y . We may use the unary predicate \underset{y}{\textup{Set}}(x) \hspace{3mm} \textup{defined by} \hspace{3mm} \exists y (x \in y), where the right-side existentially quantified membership statement means x is a set. In the absence of confusion we may omit y on the left, simply writing \textup{Set}(x) . We will say x is a proper class if it is not a set.