Consider the following premises. There is at least one y for which y will go running or y is not an artist. For all y, y is an artist or y will not drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which if y drinks water, then y is running.
 From the fact that for all y, y is an artist or y will not drink water we can infer that for all y, if y drinks water, then y is an artist via universal rewriting. From the fact that there is at least one y for which y will go running or y is not an artist we can infer that there is at least one y for which if y were an artist, then y is running via existential rewriting. Finally, from the fact that for all y, if y drinks water, then y is an artist, and that there is at least one y for which if y were an artist, then y is running we can infer that there is at least one y for which if y drinks water, then y is running via existential transitivity. Therefore, the answer is yes.