Consider the following premises. There is at least one x_5 for which x_5 is a police officer. For all x_5, x_5 will play squash. For all x_5, x_5 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will read a book and x_5 is a police officer.
 From the fact that for all x_5, x_5 will read a book, and that for all x_5, x_5 will play squash we can infer that for all x_5, x_5 will read a book and x_5 will play squash via universal conjunction. From the fact that for all x_5, x_5 will read a book and x_5 will play squash we can infer that for all x_5, x_5 will read a book via universal simplification. Finally, from the fact that for all x_5, x_5 will read a book, and that there is at least one x_5 for which x_5 is a police officer we can infer that there is at least one x_5 for which x_5 will read a book and x_5 is a police officer via existential conjunction. Therefore, the answer is yes.