[002O] Remark 4.4.2·b.

Let $\mathscr{M}$ be a model of ETCS; and let $\mathfrak{C}$ be a class of families of sets in $\mathscr{M}$. Then $\mathfrak{C}$ is a class of objects in the canonical self-indexing $\SelfIx{\mathscr{M}}$ over $\mathscr{M}$. Furthermore, $\mathscr{M}$ a definable class in $\SelfIx{\mathscr{M}}$ in the sense of Definition 4.4.2·a [002W] if and only if it is a definable class of families of sets in the sense of Definition 4.4.1·c [002P].