Is it possible that $\mathcal{X} = \mathcal{Y}$, yet $\mathcal{X} \in \mathcal{Y}$?

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Is it possible for a set to equal another set, yet the former set be an element in the latter set? I.e.:

$\mathcal{X} = \mathcal{Y}$, yet $\mathcal{X} \in \mathcal{Y}$