Consider the following premises. There is at least one y for which if y writes a letter, then y is a poet. For all y, if y were a musician, then y is listening to a song. For all y, if y were excited, then y is writing a letter. For all y, if y listens to a song, then y is excited. 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 a musician, then y is a poet.
 From the fact that for all y, if y were a musician, then y is listening to a song, and that for all y, if y listens to a song, then y is excited we can infer that for all y, if y were a musician, then y is excited via universal transitivity. From the fact that for all y, if y were excited, then y is writing a letter, and that there is at least one y for which if y writes a letter, then y is a poet we can infer that there is at least one y for which if y were excited, then y is a poet via existential transitivity. Finally, from the fact that for all y, if y were a musician, then y is excited, and that there is at least one y for which if y were excited, then y is a poet we can infer that there is at least one y for which if y were a musician, then y is a poet via existential transitivity. Therefore, the answer is yes.