Consider the following premises. For all x_5, x_5 is a scientist if and only if x_5 is an office clerk. For all x_5, x_5 is not a scientist. For all x_5, if x_5 takes a plane, then x_5 is an office clerk. There is at least one x_5 for which if x_5 were a nurse, then x_5 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is not a nurse.
 From the fact that there is at least one x_5 for which if x_5 were a nurse, then x_5 is taking a plane, and that for all x_5, if x_5 takes a plane, then x_5 is an office clerk we can infer that there is at least one x_5 for which if x_5 were a nurse, then x_5 is an office clerk via existential transitivity. From the fact that for all x_5, x_5 is a scientist if and only if x_5 is an office clerk, and that for all x_5, x_5 is not a scientist we can infer that for all x_5, x_5 is not an office clerk via universal biconditional elimination. Finally, from the fact that there is at least one x_5 for which if x_5 were a nurse, then x_5 is an office clerk, and that for all x_5, x_5 is not an office clerk we can infer that there is at least one x_5 for which x_5 is not a nurse via existential modus tollens. Therefore, the answer is yes.