Consider the following premises. There is at least one x_11 for which x_11 will play tennis or x_11 will drink water. For all x_11, if x_11 plays tennis, then x_11 is driving a car. For all x_11, if x_11 drinks water, then x_11 is driving a car. For all x_11, x_11 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is poor.
 From the fact that for all x_11, if x_11 plays tennis, then x_11 is driving a car, that for all x_11, if x_11 drinks water, then x_11 is driving a car, and that there is at least one x_11 for which x_11 will play tennis or x_11 will drink water we can infer that there is at least one x_11 for which x_11 will drive a car via existential disjunction elimination. From the fact that for all x_11, x_11 is poor, and that there is at least one x_11 for which x_11 will drive a car we can infer that there is at least one x_11 for which x_11 is poor and x_11 will drive a car via existential conjunction. Finally, from the fact that there is at least one x_11 for which x_11 is poor and x_11 will drive a car we can infer that there is at least one x_11 for which x_11 is poor via existential simplification. Therefore, the answer is yes.