Consider the following premises. For all x_8, x_8 is a writer if and only if x_8 will drive a car. There is at least one x_8 for which x_8 will drive a car if and only if x_8 will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, the fact that x_8 were a writer does not imply that x_8 is playing a game.
 From the fact that there is at least one x_8 for which x_8 will drive a car if and only if x_8 will play a game we can infer that there is at least one x_8 for which if x_8 drives a car, then x_8 is playing a game via existential biconditional elimination. Finally, from the fact that for all x_8, x_8 is a writer if and only if x_8 will drive a car we can infer that for all x_8, if x_8 were a writer, then x_8 is driving a car via universal biconditional elimination, which contradicts that For all x_8, the fact that x_8 were a writer does not imply that x_8 is playing a game. Therefore, the answer is no.