Consider the following premises. There is at least one x_6 for which x_6 will drive a car or x_6 will play a game. For all x_6, x_6 will not drive a car. For all x_6, x_6 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not play a game.
 From the fact that there is at least one x_6 for which x_6 will drive a car or x_6 will play a game, and that for all x_6, x_6 will not drive a car we can infer that there is at least one x_6 for which x_6 will play a game via existential disjunctive syllogism. From the fact that there is at least one x_6 for which x_6 will play a game, and that for all x_6, x_6 will write a letter we can infer that there is at least one x_6 for which x_6 will play a game and x_6 will write a letter via existential conjunction. Finally, from the fact that there is at least one x_6 for which x_6 will play a game and x_6 will write a letter we can infer that there is at least one x_6 for which x_6 will play a game via existential simplification, which contradicts that For all x_6, x_6 will not play a game. Therefore, the answer is no.