Consider the following premises. u_4 -> w_2. w_2 -> p. p -> u_4. w_2 <-> q_4. ~q_4. Can we infer u_4 from them? If possible, name the inference rules being used at each step.
 From w_2 -> p, p -> u_4 we can infer w_2 -> u_4 via transitivity. From w_2 -> u_4, u_4 -> w_2 we can infer w_2 <-> u_4 via biconditional introduction. From w_2 <-> q_4, ~q_4 we can infer ~w_2 via biconditional elimination. Finally, from w_2 <-> u_4, ~w_2 we can infer ~u_4 via biconditional elimination, which contradicts u_4. Therefore, the answer is no.