Consider the following premises. For all z, z will not listen to a song. There is at least one z for which if z were a sailor, then z is listening to a song. For all z, if z listens to a song, then z is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is not a sailor.
 From the fact that for all z, if z listens to a song, then z is a sailor, and that there is at least one z for which if z were a sailor, then z is listening to a song we can infer that there is at least one z for which z will listen to a song if and only if z is a sailor via existential biconditional introduction. Finally, from the fact that there is at least one z for which z will listen to a song if and only if z is a sailor, and that for all z, z will not listen to a song we can infer that there is at least one z for which z is not a sailor via existential biconditional elimination. Therefore, the answer is yes.