Consider the following premises. For all x_8, if x_8 takes a plane, then x_8 is running. There is at least one x_8 for which if x_8 were a mechanic, then x_8 is taking a plane. For all x_8, x_8 will play a game if and only if x_8 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which if x_8 plays a game, then x_8 is running.
 From the fact that for all x_8, x_8 will play a game if and only if x_8 is a mechanic we can infer that for all x_8, if x_8 plays a game, then x_8 is a mechanic via universal biconditional elimination. From the fact that there is at least one x_8 for which if x_8 were a mechanic, then x_8 is taking a plane, and that for all x_8, if x_8 takes a plane, then x_8 is running we can infer that there is at least one x_8 for which if x_8 were a mechanic, then x_8 is running via existential transitivity. Finally, from the fact that for all x_8, if x_8 plays a game, then x_8 is a mechanic, and that there is at least one x_8 for which if x_8 were a mechanic, then x_8 is running we can infer that there is at least one x_8 for which if x_8 plays a game, then x_8 is running via existential transitivity. Therefore, the answer is yes.