Membership in a Cartesian Product, and the Cartesian Product of Two Sets Is a Set

In the setting of Class Theory NBG: the Axioms, Standing Conventions and Basic Notation, let $X$ and $Y$ be classes.

¶ For all sets $u$ and $v$, the ordered pair $(u,v)$ is an element of the Cartesian product $X\times Y$ if and only if $u\in X$ and $v\in Y$.

¶ For all sets $x$ and $y$, the Cartesian product $x\times y$ is a set.