Consider the following premises. There is at least one z for which if z were excited, then z is an artist. For all z, if z were a poet, then z is excited. For all z, if z were an artist, then z is a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which if z were an artist, then z is a poet.
 From the fact that for all z, if z were a poet, then z is excited, and that there is at least one z for which if z were excited, then z is an artist we can infer that there is at least one z for which if z were a poet, then z is an artist via existential transitivity. From the fact that for all z, if z were an artist, then z is a poet, and that there is at least one z for which if z were a poet, then z is an artist we can infer that there is at least one z for which z is an artist if and only if z is a poet via existential biconditional introduction. Finally, from the fact that there is at least one z for which z is an artist if and only if z is a poet we can infer that there is at least one z for which if z were an artist, then z is a poet via existential biconditional elimination. Therefore, the answer is yes.