Consider the following premises. For all z_4, z_4 is an electrician if and only if z_4 is a nurse. For all z_4, if z_4 were a nurse, then z_4 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_4 for which the fact that z_4 were an electrician does not imply that z_4 is a nurse.
 From the fact that for all z_4, z_4 is an electrician if and only if z_4 is a nurse we can infer that for all z_4, if z_4 were an electrician, then z_4 is a nurse via universal biconditional elimination. From the fact that for all z_4, if z_4 were an electrician, then z_4 is a nurse, and that for all z_4, if z_4 were a nurse, then z_4 is an electrician we can infer that for all z_4, z_4 is an electrician if and only if z_4 is a nurse via universal biconditional introduction. Finally, from the fact that for all z_4, z_4 is an electrician if and only if z_4 is a nurse we can infer that for all z_4, if z_4 were an electrician, then z_4 is a nurse via universal biconditional elimination, which contradicts that There is at least one z_4 for which the fact that z_4 were an electrician does not imply that z_4 is a nurse. Therefore, the answer is no.