Consider the following premises. For all z, z is excited if and only if z is a nurse. For all z, if z were a scientist, then z is excited. There is at least one z for which z is a nurse if and only if z is a scientist. 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 a scientist, then z is a nurse.
 From the fact that for all z, z is excited if and only if z is a nurse we can infer that for all z, if z were excited, then z is a nurse via universal biconditional elimination. From the fact that for all z, if z were a scientist, then z is excited, and that for all z, if z were excited, then z is a nurse we can infer that for all z, if z were a scientist, then z is a nurse via universal transitivity. From the fact that there is at least one z for which z is a nurse if and only if z is a scientist we can infer that there is at least one z for which if z were a nurse, then z is a scientist via existential biconditional elimination. From the fact that for all z, if z were a scientist, then z is a nurse, and that there is at least one z for which if z were a nurse, then z is a scientist we can infer that there is at least one z for which z is a scientist if and only if z is a nurse via existential biconditional introduction. Finally, from the fact that there is at least one z for which z is a scientist if and only if z is a nurse we can infer that there is at least one z for which if z were a scientist, then z is a nurse via existential biconditional elimination. Therefore, the answer is yes.