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