Consider the following premises. There is at least one z for which z is a server if and only if z is a carpenter. For all z, z is a carpenter or z is not a server. 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 a carpenter if and only if z is a server.
 From the fact that for all z, z is a carpenter or z is not a server we can infer that for all z, if z were a server, then z is a carpenter via universal rewriting. From the fact that there is at least one z for which z is a server if and only if z is a carpenter we can infer that there is at least one z for which if z were a carpenter, then z is a server via existential biconditional elimination. Finally, from the fact that there is at least one z for which if z were a carpenter, then z is a server, and that for all z, if z were a server, then z is a carpenter we can infer that there is at least one z for which z is a carpenter if and only if z is a server via existential biconditional introduction. Therefore, the answer is yes.