Let $X = \prod_{n = 1}^N X_n$ be a D326: Cartesian product such that

(i)	$\pi_1, \ldots, \pi_N$ are each a D327: Canonical set projection on $X$
(ii)	$E \subseteq X$ is a D78: Subset of $X$

Then $(x_1, \ldots, x_N) \in E$ if and only if \begin{equation} x_1 \in \pi_1(E), \quad \ldots, \quad x_N \in \pi_N(E) \end{equation}