Consider the following premises. For all y_3, y_3 will not play a game. For all y_3, y_3 is a nurse or y_3 will not take a plane. For all y_3, y_3 is a nurse if and only if y_3 will play a game. Can we infer the following from them? There is at least one y_3 for which y_3 will take a plane.
 From the fact that for all y_3, y_3 is a nurse or y_3 will not take a plane we can infer that for all y_3, if y_3 takes a plane, then y_3 is a nurse. From the fact that for all y_3, y_3 is a nurse if and only if y_3 will play a game, and that for all y_3, y_3 will not play a game we can infer that for all y_3, y_3 is not a nurse. Finally, from the fact that for all y_3, if y_3 takes a plane, then y_3 is a nurse, and that for all y_3, y_3 is not a nurse we can infer that for all y_3, y_3 will not take a plane, which contradicts that There is at least one y_3 for which y_3 will take a plane. Therefore, the answer is no.