Consider the following premises. For all x_4, if x_4 were a lawyer, then x_4 is playing tennis. For all x_4, if x_4 plays tennis, then x_4 is not excited. There is at least one x_4 for which x_4 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 is not a lawyer.
 From the fact that for all x_4, if x_4 plays tennis, then x_4 is not excited, and that there is at least one x_4 for which x_4 is excited we can infer that there is at least one x_4 for which x_4 will not play tennis via existential modus tollens. Finally, from the fact that for all x_4, if x_4 were a lawyer, then x_4 is playing tennis, and that there is at least one x_4 for which x_4 will not play tennis we can infer that there is at least one x_4 for which x_4 is not a lawyer via existential modus tollens. Therefore, the answer is yes.