Consider the following premises. There is at least one x_1 for which x_1 will play a game if and only if x_1 is a bartender. For all x_1, x_1 is not a police officer. For all x_1, if x_1 were a bartender, then x_1 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will play a game.
 From the fact that for all x_1, if x_1 were a bartender, then x_1 is a police officer, and that for all x_1, x_1 is not a police officer we can infer that for all x_1, x_1 is not a bartender via universal modus tollens. Finally, from the fact that there is at least one x_1 for which x_1 will play a game if and only if x_1 is a bartender, and that for all x_1, x_1 is not a bartender we can infer that there is at least one x_1 for which x_1 will not play a game via existential biconditional elimination, which contradicts that For all x_1, x_1 will play a game. Therefore, the answer is no.