Consider the following premises. There is at least one x_3 for which if x_3 were excited, then x_3 is an office clerk. For all x_3, x_3 is not an office clerk. For all x_3, if x_3 were an office clerk, then x_3 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is not excited.
 From the fact that there is at least one x_3 for which if x_3 were excited, then x_3 is an office clerk, and that for all x_3, if x_3 were an office clerk, then x_3 is excited we can infer that there is at least one x_3 for which x_3 is excited if and only if x_3 is an office clerk via existential biconditional introduction. From the fact that there is at least one x_3 for which x_3 is excited if and only if x_3 is an office clerk we can infer that there is at least one x_3 for which if x_3 were excited, then x_3 is an office clerk via existential biconditional elimination. Finally, from the fact that there is at least one x_3 for which if x_3 were excited, then x_3 is an office clerk, and that for all x_3, x_3 is not an office clerk we can infer that there is at least one x_3 for which x_3 is not excited via existential modus tollens. Therefore, the answer is yes.