Descending chain of characteristic subgroups of free group has trivial intersection

Definition
Suppose $$F$$ is a free group and $$H_0 = F \ge H_1 \ge H_2 \ge \dots$$ is a strictly descending chain of characteristic subgroups of $$F$$, indexed by the nonnegative integers. Then, the intersection of the $$H_n$$s is trivial.