Consider the following premises. For all y_1, y_1 is sad and y_1 will climb a mountain. There is at least one y_1 for which y_1 is sad if and only if y_1 is poor. Can we infer the following from them? There is at least one y_1 for which y_1 is poor.
 From the fact that there is at least one y_1 for which y_1 is sad if and only if y_1 is poor we can infer that there is at least one y_1 for which if y_1 were sad, then y_1 is poor. From the fact that for all y_1, y_1 is sad and y_1 will climb a mountain we can infer that for all y_1, y_1 is sad. Finally, from the fact that there is at least one y_1 for which if y_1 were sad, then y_1 is poor, and that for all y_1, y_1 is sad we can infer that there is at least one y_1 for which y_1 is poor. Therefore, the answer is yes.