Consider the following premises. If Susan were a scientist, then it is overcast. It is not overcast. For all x_9, x_9 is a scientist if and only if x_9 is poor. If it is overcast, then Susan is a scientist. Can we infer the following from them? If we can, name the inference rule being used: Susan is not poor.
 From the fact that for all x_9, x_9 is a scientist if and only if x_9 is poor we can infer that Susan is a scientist if and only if Susan is poor via universal instantiation. From the fact that if Susan were a scientist, then it is overcast, and that if it is overcast, then Susan is a scientist we can infer that Susan is a scientist if and only if it is overcast via biconditional introduction. From the fact that Susan is a scientist if and only if it is overcast, and that it is not overcast we can infer that Susan is not a scientist via biconditional elimination. Finally, from the fact that Susan is a scientist if and only if Susan is poor, and that Susan is not a scientist we can infer that Susan is not poor via biconditional elimination. Therefore, the answer is yes.