Consider the following premises. ~u. u -> w. w <-> u. u_3 <-> w. Can we infer ~u_3 from them? If possible, name the inference rules being used at each step.
 From w <-> u we can infer w -> u via biconditional elimination. From w -> u, u -> w we can infer w <-> u via biconditional introduction. From w <-> u, ~u we can infer ~w via biconditional elimination. Finally, from u_3 <-> w, ~w we can infer ~u_3 via biconditional elimination. Therefore, the answer is yes.