Consider the following premises. There is at least one z_3 for which if z_3 were a server, then z_3 is a mechanic. For all z_3, z_3 is a server if and only if z_3 is a mechanic. For all z_3, z_3 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_3 for which z_3 is not a mechanic.
 From the fact that for all z_3, z_3 is a server if and only if z_3 is a mechanic we can infer that for all z_3, if z_3 were a mechanic, then z_3 is a server via universal biconditional elimination. From the fact that for all z_3, if z_3 were a mechanic, then z_3 is a server, and that there is at least one z_3 for which if z_3 were a server, then z_3 is a mechanic we can infer that there is at least one z_3 for which z_3 is a mechanic if and only if z_3 is a server via existential biconditional introduction. Finally, from the fact that there is at least one z_3 for which z_3 is a mechanic if and only if z_3 is a server, and that for all z_3, z_3 is not a server we can infer that there is at least one z_3 for which z_3 is not a mechanic via existential biconditional elimination. Therefore, the answer is yes.