Consider the following premises. u -> w. ~u. ~w -> u_2. w -> u. Can we infer u_2 or r_3 from them? If possible, name the inference rules being used at each step.
 From u -> w, w -> u we can infer u <-> w via biconditional introduction. From u <-> w, ~u we can infer ~w via biconditional elimination. From ~w -> u_2, ~w we can infer u_2 via modus ponens. Finally, from u_2 we can infer u_2 or r_3 via addition. Therefore, the answer is yes.