Consider the following premises. There is at least one x_7 for which x_7 is a nurse. For all x_7, if x_7 were a nurse, then x_7 is a scientist. For all x_7, x_7 is a cashier and x_7 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: Some cashiers are scientists.
 From the fact that for all x_7, if x_7 were a nurse, then x_7 is a scientist, and that there is at least one x_7 for which x_7 is a nurse we can infer that there is at least one x_7 for which x_7 is a scientist via existential modus ponens. From the fact that for all x_7, x_7 is a cashier and x_7 is a soldier we can infer that for all x_7, x_7 is a cashier via universal simplification. Finally, from the fact that for all x_7, x_7 is a cashier, and that there is at least one x_7 for which x_7 is a scientist we can infer that some cashiers are scientists via existential conjunction. Therefore, the answer is yes.