Consider the following premises. For all x_7, if x_7 plays a game, then x_7 is driving a car. For all x_7, x_7 is an artist and x_7 is a police officer. There is at least one x_7 for which x_7 will play a game. 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 is an artist and x_7 will drive a car.
 From the fact that for all x_7, if x_7 plays a game, then x_7 is driving a car, and that there is at least one x_7 for which x_7 will play a game we can infer that there is at least one x_7 for which x_7 will drive a car via existential modus ponens. From the fact that for all x_7, x_7 is an artist and x_7 is a police officer we can infer that for all x_7, x_7 is an artist via universal simplification. Finally, from the fact that for all x_7, x_7 is an artist, and that there is at least one x_7 for which x_7 will drive a car we can infer that there is at least one x_7 for which x_7 is an artist and x_7 will drive a car via existential conjunction. Therefore, the answer is yes.