Consider the following premises. For all y, y is a poet if and only if y is an artist. For all y, if y were an artist, then y is a poet. For all y, y is a poet 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 is not true that y is a poet if and only if y is an artist.
 From the fact that for all y, y is a poet or y is not an artist we can infer that for all y, if y were an artist, then y is a poet via universal rewriting. From the fact that for all y, y is a poet if and only if y is an artist we can infer that for all y, if y were a poet, then y is an artist via universal biconditional elimination. From the fact that for all y, if y were an artist, then y is a poet, and that for all y, if y were a poet, then y is an artist we can infer that for all y, y is an artist if and only if y is a poet via universal biconditional introduction. From the fact that for all y, y is an artist if and only if y is a poet we can infer that for all y, if y were a poet, then y is an artist via universal biconditional elimination. Finally, from the fact that for all y, if y were a poet, then y is an artist, and that for all y, if y were an artist, then y is a poet we can infer that for all y, y is a poet if and only if y is an artist via universal biconditional introduction, which contradicts that There is at least one y for which if is not true that y is a poet if and only if y is an artist. Therefore, the answer is no.