Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that

(i)	$E \subseteq X$ is a D78: Subset of $X$

By definition \begin{equation} \text{int} \langle E \rangle : = \bigcup \{ U \in \mathcal{T} : U \subseteq E \} \end{equation} Since every set in the union $\text{int} \langle E \rangle$ is required to be contained in $E$, then result R4152: implies the inclusion $\text{int} \langle E \rangle \subseteq E$, as claimed. $\square$