Consider the following premises. For all x_4, x_4 is fast if and only if x_4 will play a game. There is at least one x_4 for which if x_4 were fast, then x_4 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will play a game if and only if x_4 is fast.
 From the fact that for all x_4, x_4 is fast if and only if x_4 will play a game we can infer that for all x_4, if x_4 plays a game, then x_4 is fast via universal biconditional elimination. Finally, from the fact that for all x_4, if x_4 plays a game, then x_4 is fast, and that there is at least one x_4 for which if x_4 were fast, then x_4 is playing a game we can infer that there is at least one x_4 for which x_4 will play a game if and only if x_4 is fast via existential biconditional introduction. Therefore, the answer is yes.