Consider the following premises. For all x_9, x_9 will take a plane if and only if x_9 will cook. For all x_9, x_9 is a writer. For all x_9, if x_9 were a writer, then x_9 is playing a game. For all x_9, if x_9 plays a game, then x_9 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will cook.
 From the fact that for all x_9, if x_9 were a writer, then x_9 is playing a game, and that for all x_9, if x_9 plays a game, then x_9 is taking a plane we can infer that for all x_9, if x_9 were a writer, then x_9 is taking a plane via universal transitivity. From the fact that for all x_9, x_9 will take a plane if and only if x_9 will cook we can infer that for all x_9, if x_9 takes a plane, then x_9 is cooking via universal biconditional elimination. From the fact that for all x_9, if x_9 were a writer, then x_9 is taking a plane, and that for all x_9, x_9 is a writer we can infer that for all x_9, x_9 will take a plane via universal modus ponens. Finally, from the fact that for all x_9, if x_9 takes a plane, then x_9 is cooking, and that for all x_9, x_9 will take a plane we can infer that for all x_9, x_9 will cook via universal modus ponens. Therefore, the answer is yes.