Consider the following premises. It is cold if and only if Joseph is a lawyer. For all z, z is a carpenter. If it is cold, then Robert is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not a lawyer.
 From the fact that for all z, z is a carpenter we can infer that Robert is a carpenter via universal instantiation. From the fact that if it is cold, then Robert is not a carpenter, and that Robert is a carpenter we can infer that it is not cold via modus tollens. Finally, from the fact that it is cold if and only if Joseph is a lawyer, and that it is not cold we can infer that Joseph is not a lawyer via biconditional elimination. Therefore, the answer is yes.