Consider the following premises. For all x_3, x_3 will go running and x_3 will climb a mountain. There is at least one x_3 for which x_3 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 will go running and x_3 is a police officer.
 From the fact that for all x_3, x_3 will go running and x_3 will climb a mountain we can infer that for all x_3, x_3 will go running via universal simplification. Finally, from the fact that for all x_3, x_3 will go running, and that there is at least one x_3 for which x_3 is a police officer we can infer that there is at least one x_3 for which x_3 will go running and x_3 is a police officer via existential conjunction. Therefore, the answer is yes.