Is this a unary operation or simply a declaration?

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In another question, I was told that I was performing a unary operation by saying:

Let $\Bbb{X}$ be a non-empty subset of $\Bbb{R}$ and closed under division. It follows that: $$k\in\Bbb{X}\iff\frac{1}{k}\in\Bbb{X}$$

Is this a unary operation of $k$ or simply a logical statement? And if the former is the case, is it $\in$ or $\iff$ that is the operation?