Let $X$ be a D11: Set such that

(i)	$\mathcal{F} \subseteq \mathcal{P}(X)$ is a D84: Sigma-algebra on $X$

A D11: Set $\mathcal{G}$ is a subsigma-algebra of $\mathcal{F}$ on $X$ if and only if

(1)	\begin{equation} \mathcal{G} \subseteq \mathcal{F} \end{equation}
(2)	$\mathcal{G}$ is a D84: Sigma-algebra on $X$