Consider the following premises. There is at least one x_1 for which if x_1 were a doctor, then x_1 is happy. For all x_1, if x_1 were a cashier, then x_1 is a doctor. For all x_1, x_1 is not happy. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 is not a cashier.
 From the fact that there is at least one x_1 for which if x_1 were a doctor, then x_1 is happy, and that for all x_1, x_1 is not happy we can infer that there is at least one x_1 for which x_1 is not a doctor via existential modus tollens. Finally, from the fact that for all x_1, if x_1 were a cashier, then x_1 is a doctor, and that there is at least one x_1 for which x_1 is not a doctor we can infer that there is at least one x_1 for which x_1 is not a cashier via existential modus tollens. Therefore, the answer is yes.