Consider the following premises. ~u. w <-> u. u -> w. u_3 <-> w. Can we infer ~u_3 from them?
 From w <-> u we can infer w -> u. From w -> u, u -> w we can infer w <-> u. From w <-> u, ~u we can infer ~w. Finally, from u_3 <-> w, ~w we can infer ~u_3. Therefore, the answer is yes.