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