Consider the following premises. For all x_10, x_10 will sleep. For all x_10, x_10 is a soldier. There is at least one x_10 for which if x_10 sleeps, then x_10 is poor. For all x_10, if x_10 were a cashier, then x_10 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is poor and x_10 is a soldier.
 From the fact that for all x_10, x_10 will sleep we can infer that for all x_10, x_10 will sleep or x_10 is a cashier via universal addition. From the fact that there is at least one x_10 for which if x_10 sleeps, then x_10 is poor, that for all x_10, if x_10 were a cashier, then x_10 is poor, and that for all x_10, x_10 will sleep or x_10 is a cashier we can infer that there is at least one x_10 for which x_10 is poor via existential disjunction elimination. Finally, from the fact that there is at least one x_10 for which x_10 is poor, and that for all x_10, x_10 is a soldier we can infer that there is at least one x_10 for which x_10 is poor and x_10 is a soldier via existential conjunction. Therefore, the answer is yes.