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:

$$\forall x \in S: \left[\left[{x}\right]\right]_{\mathcal{R}} \subseteq S$$