Consider the following premises. For all y, y is an artist or y will not write a letter. There is at least one y for which y will write a letter if and only if y will go running. Can we infer the following from them? There is at least one y for which if y goes running, then y is an artist.
 From the fact that for all y, y is an artist or y will not write a letter we can infer that for all y, if y writes a letter, then y is an artist. From the fact that there is at least one y for which y will write a letter if and only if y will go running we can infer that there is at least one y for which if y goes running, then y is writing a letter. Finally, from the fact that there is at least one y for which if y goes running, then y is writing a letter, and that for all y, if y writes a letter, then y is an artist we can infer that there is at least one y for which if y goes running, then y is an artist. Therefore, the answer is yes.