Suppose $\hat F_n(y)\overset{p}\to F(y)$, can we obtain $\sup_y|\hat F_n(y)-F(y)|\overset{p}\to0$?

Question

If we have

(i) $\hat F_n(y)\overset{p}\to F(y)$;

(ii) $|F(y)|\le1$;

(iii) $F(y)$ is a monotonically increasing function with respect to $y$.

Can we obtain the following result directly $$\sup_y|\hat F_n(y)-F(y)|\overset{p}\to0?$$