Consider the following premises. Sarah is a politician if and only if it is overcast. It is cold if and only if it is overcast. Sarah is not a politician. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that Sarah is a politician if and only if it is overcast, and that Sarah is not a politician we can infer that it is not overcast via biconditional elimination. Finally, from the fact that it is cold if and only if it is overcast, and that it is not overcast we can infer that it is not cold via biconditional elimination, which contradicts that It is cold. Therefore, the answer is no.