Consider the following premises. For all x_8, x_8 is sad or x_8 will play tennis. There is at least one x_8 for which x_8 is sad if and only if x_8 will play a game. For all x_8, x_8 will play a game or x_8 will not play tennis. 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 x_8 will play a game.
 From the fact that there is at least one x_8 for which x_8 is sad 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 were sad, then x_8 is playing a game via existential biconditional elimination. From the fact that for all x_8, x_8 will play a game or x_8 will not play tennis we can infer that for all x_8, if x_8 plays tennis, then x_8 is playing a game via universal rewriting. Finally, from the fact that there is at least one x_8 for which if x_8 were sad, then x_8 is playing a game, that for all x_8, if x_8 plays tennis, then x_8 is playing a game, and that for all x_8, x_8 is sad or x_8 will play tennis we can infer that there is at least one x_8 for which x_8 will play a game via existential disjunction elimination. Therefore, the answer is yes.