Consider the following premises. There is at least one x_7 for which x_7 will drink water. For all x_7, if x_7 were a politician, then x_7 is driving a car. For all x_7, x_7 is a politician and x_7 is a mechanic. 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 drive a car and x_7 will drink water.
 From the fact that for all x_7, x_7 is a politician and x_7 is a mechanic we can infer that for all x_7, x_7 is a politician via universal simplification. From the fact that for all x_7, if x_7 were a politician, then x_7 is driving a car, and that for all x_7, x_7 is a politician we can infer that for all x_7, x_7 will drive a car via universal modus ponens. Finally, from the fact that for all x_7, x_7 will drive a car, and that there is at least one x_7 for which x_7 will drink water we can infer that there is at least one x_7 for which x_7 will drive a car and x_7 will drink water via existential conjunction. Therefore, the answer is yes.