Consider the following premises. If Barbara were a lawyer, then it is late. It is overcast if and only if it is late. Barbara is a lawyer if and only if it is overcast. Can we infer the following from them? If we can, name the inference rule being used: The fact that Barbara were a lawyer does not imply that it is overcast.
 From the fact that it is overcast if and only if it is late we can infer that if it is late, then it is overcast via biconditional elimination. From the fact that Barbara is a lawyer if and only if it is overcast we can infer that if it is overcast, then Barbara is a lawyer via biconditional elimination. Finally, from the fact that if Barbara were a lawyer, then it is late, and that if it is late, then it is overcast we can infer that if Barbara were a lawyer, then it is overcast via transitivity, which contradicts that The fact that Barbara were a lawyer does not imply that it is overcast. Therefore, the answer is no.