Consider the following premises. For all x_12, x_12 will listen to a song. For all x_12, x_12 will make tea and x_12 will play a game. There is at least one x_12 for which if x_12 listens to a song, then x_12 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will make tea and x_12 is excited.
 From the fact that for all x_12, x_12 will make tea and x_12 will play a game we can infer that for all x_12, x_12 will make tea via universal simplification. From the fact that there is at least one x_12 for which if x_12 listens to a song, then x_12 is excited, and that for all x_12, x_12 will listen to a song we can infer that there is at least one x_12 for which x_12 is excited via existential modus ponens. Finally, from the fact that for all x_12, x_12 will make tea, and that there is at least one x_12 for which x_12 is excited we can infer that there is at least one x_12 for which x_12 will make tea and x_12 is excited via existential conjunction. Therefore, the answer is yes.