We show that in set theory without the axiom of choice ZF, the statement sH: “Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it” implies AC${}^{\mathrm{fin}}$, the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC${}^{\mathrm{fin}}$ in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?