Consider the following premises. For all x_2, x_2 is a poet or x_2 will play a game. There is at least one x_2 for which if x_2 plays a game, then x_2 is a police officer. For all x_2, x_2 is a police officer or x_2 is not a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 is a police officer.
 From the fact that for all x_2, x_2 is a police officer or x_2 is not a poet we can infer that for all x_2, if x_2 were a poet, then x_2 is a police officer via universal rewriting. Finally, from the fact that for all x_2, if x_2 were a poet, then x_2 is a police officer, that there is at least one x_2 for which if x_2 plays a game, then x_2 is a police officer, and that for all x_2, x_2 is a poet or x_2 will play a game we can infer that there is at least one x_2 for which x_2 is a police officer via existential disjunction elimination. Therefore, the answer is yes.