Consider the following premises. For all x_4, if x_4 were a taxi driver, then x_4 is a nurse. For all x_4, x_4 is a taxi driver or x_4 is a doctor. For all x_4, if x_4 were a server, then x_4 is not a nurse. For all x_4, if x_4 were a doctor, then x_4 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is not a server.
 From the fact that for all x_4, if x_4 were a taxi driver, then x_4 is a nurse, that for all x_4, if x_4 were a doctor, then x_4 is a nurse, and that for all x_4, x_4 is a taxi driver or x_4 is a doctor we can infer that for all x_4, x_4 is a nurse via universal disjunction elimination. Finally, from the fact that for all x_4, if x_4 were a server, then x_4 is not a nurse, and that for all x_4, x_4 is a nurse we can infer that for all x_4, x_4 is not a server via universal modus tollens. Therefore, the answer is yes.