Consider the following premises. It is overcast if and only if Susan is a doctor. For all x, x is a doctor if and only if x will work. Susan is not working. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that for all x, x is a doctor if and only if x will work we can infer that Susan is a doctor if and only if Susan is working via universal instantiation. From the fact that Susan is a doctor if and only if Susan is working, and that Susan is not working we can infer that Susan is not a doctor via biconditional elimination. Finally, from the fact that it is overcast if and only if Susan is a doctor, and that Susan is not a doctor we can infer that it is not overcast via biconditional elimination. Therefore, the answer is yes.