Consider the following premises. For all z, z is a cashier if and only if z is a lawyer. There is at least one z for which z is a politician if and only if z is a lawyer. For all z, z is not a cashier. 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 politician.
 From the fact that for all z, z is a cashier if and only if z is a lawyer, and that for all z, z is not a cashier we can infer that for all z, z is not a lawyer via universal biconditional elimination. Finally, from the fact that there is at least one z for which z is a politician if and only if z is a lawyer, and that for all z, z is not a lawyer we can infer that there is at least one z for which z is not a politician via existential biconditional elimination. Therefore, the answer is yes.