Consider the following premises. For all x_7, x_7 is not rich. For all x_7, x_7 will work if and only if x_7 is rich. For all x_7, if x_7 plays a game, then x_7 is working. Can we infer the following from them? There is at least one x_7 for which x_7 will play a game.
 From the fact that for all x_7, x_7 will work if and only if x_7 is rich we can infer that for all x_7, if x_7 works, then x_7 is rich. From the fact that for all x_7, if x_7 plays a game, then x_7 is working, and that for all x_7, if x_7 works, then x_7 is rich we can infer that for all x_7, if x_7 plays a game, then x_7 is rich. Finally, from the fact that for all x_7, if x_7 plays a game, then x_7 is rich, and that for all x_7, x_7 is not rich we can infer that for all x_7, x_7 will not play a game, which contradicts that There is at least one x_7 for which x_7 will play a game. Therefore, the answer is no.