If $- E$ is empty, then the claim is a consequence of result R7: Empty set is subset of every set, so assume that $- E \neq \emptyset$. If $x \in - E$, then $x = - e$ for some $e \in E$. Since $E \subseteq F$, then $e \in F$ and thus $x = - e \in - F$. Since $x \in - E$ was arbitrary, we are done. $\square$