Consider the following premises. For all y, if y were an office clerk, then y is a cashier. For all y, y is a cashier if and only if y is an office clerk. For all y, if y were a cashier, then y is an office clerk. Can we infer the following from them? For all y, y is a cashier if and only if y is an office clerk.
That is one of the premises. Therefore, the answer is yes.