Consider the following premises. w_4 -> p_10. u_4 -> w_4. p_10 <-> u_4. Can we infer ~(p_10 -> w_4) from them? If possible, name the inference rules being used at each step.
 From p_10 <-> u_4 we can infer p_10 -> u_4 via biconditional elimination. Finally, from p_10 -> u_4, u_4 -> w_4 we can infer p_10 -> w_4 via transitivity, which contradicts ~(p_10 -> w_4). Therefore, the answer is no.