Consider the following premises. For all z, z is a writer if and only if z is a lawyer. For all z, z is a writer or z is a taxi driver. For all z, z is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is a taxi driver.
 From the fact that for all z, z is a writer if and only if z is a lawyer we can infer that for all z, if z were a writer, then z is a lawyer via universal biconditional elimination. From the fact that for all z, if z were a writer, then z is a lawyer, and that for all z, z is not a lawyer we can infer that for all z, z is not a writer via universal modus tollens. Finally, from the fact that for all z, z is a writer or z is a taxi driver, and that for all z, z is not a writer we can infer that for all z, z is a taxi driver via universal disjunctive syllogism. Therefore, the answer is yes.