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

Proof
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