Consider the following premises. For all x_11, x_11 will play a game. For all x_11, x_11 will write a letter or x_11 will not drive a car. There is at least one x_11 for which x_11 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will play a game and x_11 will write a letter.
 From the fact that for all x_11, x_11 will write a letter or x_11 will not drive a car we can infer that for all x_11, if x_11 drives a car, then x_11 is writing a letter via universal rewriting. From the fact that for all x_11, if x_11 drives a car, then x_11 is writing a letter, and that there is at least one x_11 for which x_11 will drive a car we can infer that there is at least one x_11 for which x_11 will write a letter via existential modus ponens. Finally, from the fact that for all x_11, x_11 will play a game, and that there is at least one x_11 for which x_11 will write a letter we can infer that there is at least one x_11 for which x_11 will play a game and x_11 will write a letter via existential conjunction. Therefore, the answer is yes.