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Let $A$ be a subset of a topological space $X$ and let $B$ be a subset of $A$. I need to prove that the $\mathrm{Cl}(A)-\mathrm{Cl}(B)$ is contained in $\mathrm{Cl}(A-B)$. $\mathrm{Cl}$ denotes the closure of a set.

I first let $x$ be in $\mathrm{Cl}(A)-\mathrm{Cl}(B)$, then $x$ is in $\mathrm{Cl}(A)-B$.

After that step I'm not sure how to proceed. Any help would be deeply appreciated.

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