Consider the following premises. For all x_3, x_3 is not an artist. For all x_3, x_3 is an artist if and only if x_3 is a scientist. There is at least one x_3 for which x_3 is a scientist if and only if x_3 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is not a nurse.
 From the fact that for all x_3, x_3 is an artist if and only if x_3 is a scientist, and that for all x_3, x_3 is not an artist we can infer that for all x_3, x_3 is not a scientist via universal biconditional elimination. Finally, from the fact that there is at least one x_3 for which x_3 is a scientist if and only if x_3 is a nurse, and that for all x_3, x_3 is not a scientist we can infer that there is at least one x_3 for which x_3 is not a nurse via existential biconditional elimination. Therefore, the answer is yes.