Let $G_X = (X, \mathcal{E}_X)$ be a D778: Graph.
An D548: Ordered pair $G_E = (E, \mathcal{E}_E)$ is a subgraph of $G_X$ if and only if

(1)	$E \subseteq X$ (D78: Subset)
(2)	$\mathcal{E}_E \subseteq \mathcal{E}_X$ (D78: Subset)