Let $X$ be a D11: Set such that

(i)	$\mathsf{SA} = \mathsf{SA}(X)$ is the D484: Set of sigma-algebras on $X$
(ii)	$\mathcal{F} \in \mathsf{SA}$ is a D84: Sigma-algebra on $X$

The set of subsigma-algebras of $\mathcal{F}$ on $X$ is the D11: Set \begin{equation} \{ \mathcal{G} \in \mathsf{SA} : \mathcal{G} \subseteq \mathcal{F} \} \end{equation}