Is following proof of $\exists X \forall Y \exists Z .(X\subseteq Y \cap Z) $ valid?

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I have to make or deny proof for : $\exists X \forall Y \exists Z .(X\subseteq Y \cap Z) $

Is the proof by saying that $\emptyset \subseteq All$ and so $X = \emptyset$
enough?

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Yes it is, there is no trick question.