Consider the following premises. For all y, y is bored if and only if y is an artist. There is at least one y for which y is bored or y is not an artist. 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 were bored, then y is an artist.
 From the fact that there is at least one y for which y is bored 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 bored via existential rewriting. From the fact that for all y, y is bored if and only if y is an artist we can infer that for all y, if y were bored, then y is an artist via universal biconditional elimination. From the fact that for all y, if y were bored, then y is an artist, and that there is at least one y for which if y were an artist, then y is bored we can infer that there is at least one y for which y is bored if and only if y is an artist via existential biconditional introduction. Finally, from the fact that there is at least one y for which y is bored if and only if y is an artist we can infer that there is at least one y for which if y were bored, then y is an artist via existential biconditional elimination. Therefore, the answer is yes.