Is there a reference for the following?

Consider quasi-categories $I,C$. Suppose that a morphism between functors $\alpha : \Delta^1 \to Fun(I,C)$ is given. Suppose that for every $i \in I$, denoting the evaluation $ev_i : Fun(I,C) \to C$, the composition $ev_i \circ \alpha$ is an isomorphism (in the homotopy category). How to show then that $\alpha$ is an isomorphism (in the homotopy category)?

Thanks