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