Let $E$ be a finite set and let $\operatorname{cl}:2^E\to 2^E$ satisfy, for all $A,B\subset E$ and $e,f\in E$: $A\subset \operatorname{cl}(A)$; if $A\subset B$, then $\operatorname{cl}(A)\subset \operatorname{cl}(B)$; $\operatorname{cl}(\operatorname{cl}(A))=\operatorname{cl}(A)$; and if $f\in \operatorname{cl}(A\cup\{e\})\setminus \operatorname{cl}(A)$, then $e\in \operatorname{cl}(A\cup\{f\})$. Then the subsets $I\subset E$ satisfying $e\notin \operatorname{cl}(I\setminus\{e\})$ for every $e\in I$ are the independent sets of a matroid.