Consider the following premises. If William were not bored, then it is overcast. If William were bored, then it is late. William is bored if and only if it is late. It is not late. Can we infer the following from them? If we can, name the inference rule being used: It is overcast.
 From the fact that William is bored if and only if it is late we can infer that if it is late, then William is bored via biconditional elimination. From the fact that if it is late, then William is bored, and that if William were bored, then it is late we can infer that it is late if and only if William is bored via biconditional introduction. From the fact that it is late if and only if William is bored, and that it is not late we can infer that William is not bored via biconditional elimination. Finally, from the fact that if William were not bored, then it is overcast, and that William is not bored we can infer that it is overcast via modus ponens. Therefore, the answer is yes.