Consider the following premises. For all x_10, if x_10 makes tea, then x_10 is playing a game. For all x_10, x_10 is a server. For all x_10, if x_10 were a server, then x_10 is a writer. There is at least one x_10 for which if x_10 were a writer, then x_10 is making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will play a game.
 From the fact that for all x_10, if x_10 were a server, then x_10 is a writer, and that for all x_10, x_10 is a server we can infer that for all x_10, x_10 is a writer via universal modus ponens. From the fact that there is at least one x_10 for which if x_10 were a writer, then x_10 is making tea, and that for all x_10, x_10 is a writer we can infer that there is at least one x_10 for which x_10 will make tea via existential modus ponens. Finally, from the fact that for all x_10, if x_10 makes tea, then x_10 is playing a game, and that there is at least one x_10 for which x_10 will make tea we can infer that there is at least one x_10 for which x_10 will play a game via existential modus ponens. Therefore, the answer is yes.