Let $M=(E,\mathcal I)$ be a matroid on a finite ground set $E$ with rank function $r$, and let $A_1,\dots,A_m \subset E$. There exist distinct elements $x_i \in A_i$ such that $\{x_1,\dots,x_m\}\in\mathcal I$ if and only if $r\left(\bigcup_{i\in J} A_i\right) \ge |J|$ for every $J \subset \{1,\dots,m\}$.