Consider the following premises. For all x_7, x_7 will not play tennis. There is at least one x_7 for which x_7 is rich. For all x_7, x_7 will play tennis if and only if x_7 is a police officer. For all x_7, x_7 is a police officer or x_7 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is a nurse and x_7 is rich.
 From the fact that for all x_7, x_7 will play tennis if and only if x_7 is a police officer, and that for all x_7, x_7 will not play tennis we can infer that for all x_7, x_7 is not a police officer via universal biconditional elimination. From the fact that for all x_7, x_7 is a police officer or x_7 is a nurse, and that for all x_7, x_7 is not a police officer we can infer that for all x_7, x_7 is a nurse via universal disjunctive syllogism. Finally, from the fact that for all x_7, x_7 is a nurse, and that there is at least one x_7 for which x_7 is rich we can infer that there is at least one x_7 for which x_7 is a nurse and x_7 is rich via existential conjunction. Therefore, the answer is yes.