Consider the following premises. ~w. ~u_3 -> r_3. w <-> u. u_3 <-> u. Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From w <-> u, ~w we can infer ~u via biconditional elimination. From u_3 <-> u, ~u we can infer ~u_3 via biconditional elimination. Finally, from ~u_3 -> r_3, ~u_3 we can infer r_3 via modus ponens. Therefore, the answer is yes.