Element in its own Equivalence Class

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

Then every element of $$S$$ is in its own $\mathcal{R}$-class:
 * $$\forall x \in S: x \in \left[\!\left[{x}\right]\!\right]_{\mathcal{R}}$$

Proof
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