[05UF] Proof. This follows from (3.6) and (3.9), together with the fact that (NC){hoequiv}(NC)_{\hoequiv} is isomorphic to nerveiso(CI[1])\nerve\iso(C^{I[1]}) and the fact that the natural inclusion isoC→iso(CI[1])\iso C\rightarrow\iso(C^{I[1]}) is an equivalence of categories. ∎