Consider the following premises. For all z_4, z_4 is rich or z_4 is a janitor. There is at least one z_4 for which z_4 is a janitor if and only if z_4 is a lawyer. For all z_4, if z_4 were rich, then z_4 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all z_4, z_4 is not a lawyer.
 From the fact that there is at least one z_4 for which z_4 is a janitor if and only if z_4 is a lawyer we can infer that there is at least one z_4 for which if z_4 were a janitor, then z_4 is a lawyer via existential biconditional elimination. Finally, from the fact that for all z_4, if z_4 were rich, then z_4 is a lawyer, that there is at least one z_4 for which if z_4 were a janitor, then z_4 is a lawyer, and that for all z_4, z_4 is rich or z_4 is a janitor we can infer that there is at least one z_4 for which z_4 is a lawyer via existential disjunction elimination, which contradicts that For all z_4, z_4 is not a lawyer. Therefore, the answer is no.