Consider the following premises. For all y_1, if y_1 were poor, then y_1 is not playing a game. There is at least one y_1 for which if y_1 were a doctor, then y_1 is poor. For all y_1, y_1 will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all y_1, y_1 is a doctor.
 From the fact that for all y_1, if y_1 were poor, then y_1 is not playing a game, and that for all y_1, y_1 will play a game we can infer that for all y_1, y_1 is not poor via universal modus tollens. Finally, from the fact that there is at least one y_1 for which if y_1 were a doctor, then y_1 is poor, and that for all y_1, y_1 is not poor we can infer that there is at least one y_1 for which y_1 is not a doctor via existential modus tollens, which contradicts that For all y_1, y_1 is a doctor. Therefore, the answer is no.