Equivalence Class of Element is Subset

Theorem
Let $\mathcal R$ be an equivalence relation on a set $S$.

The $\mathcal R$-class of every element of $S$ is a subset of the set the element is in:
 * $\forall x \in S: \left[\!\left[{x}\right]\!\right]_\mathcal R \subseteq S$