Consider the following premises. For all x_8, x_8 is a writer. For all x_8, if x_8 plays a game, then x_8 is poor. For all x_8, x_8 is poor if and only if x_8 will play a game. For all x_8, if x_8 plays a game, then x_8 is not a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not poor.
 From the fact that for all x_8, x_8 is poor if and only if x_8 will play a game we can infer that for all x_8, if x_8 were poor, then x_8 is playing a game via universal biconditional elimination. From the fact that for all x_8, if x_8 plays a game, then x_8 is poor, and that for all x_8, if x_8 were poor, then x_8 is playing a game we can infer that for all x_8, x_8 will play a game if and only if x_8 is poor via universal biconditional introduction. From the fact that for all x_8, if x_8 plays a game, then x_8 is not a writer, and that for all x_8, x_8 is a writer we can infer that for all x_8, x_8 will not play a game via universal modus tollens. Finally, from the fact that for all x_8, x_8 will play a game if and only if x_8 is poor, and that for all x_8, x_8 will not play a game we can infer that for all x_8, x_8 is not poor via universal biconditional elimination. Therefore, the answer is yes.