Symmetry of Relations is Symmetric

Theorem
Let $$\mathcal{R}$$ be a relation on $$S$$ which is symmetric. Then:
 * $$\left({x, y}\right) \in \mathcal{R} \iff \left({y, x}\right) \in \mathcal{R}$$.

Proof
Let $$\mathcal{R}$$ be symmetric.

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