Consider the following premises. For all x_7, if x_7 goes running, then x_7 is making tea. For all x_7, x_7 will work. For all x_7, if x_7 works, then x_7 is drinking water. There is at least one x_7 for which x_7 will go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will make tea and x_7 will drink water.
 From the fact that for all x_7, if x_7 goes running, then x_7 is making tea, and that there is at least one x_7 for which x_7 will go running we can infer that there is at least one x_7 for which x_7 will make tea via existential modus ponens. From the fact that for all x_7, if x_7 works, then x_7 is drinking water, and that for all x_7, x_7 will work we can infer that for all x_7, x_7 will drink water via universal modus ponens. Finally, from the fact that there is at least one x_7 for which x_7 will make tea, and that for all x_7, x_7 will drink water we can infer that there is at least one x_7 for which x_7 will make tea and x_7 will drink water via existential conjunction. Therefore, the answer is yes.