If $D$ is $\|.\|-$separable subset of $X$. Then $D$ is Suslin space?

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Let $(X,\|.\|)$ be a Banach space and $\{A_n\}$ be a sequence of $\|.\|-$separable subset of $X$.

Take $D=\overline{\text{co}}~\cup_nA_n$, then $D$ is $\|.\|-$separable subset of $X$.

Question:

Why $D$ is Suslin space ?