Consider the following premises. There is at least one x for which x will work if and only if x is a cashier. For all x, x is a cashier if and only if x will work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is a cashier if and only if x will work.
 From the fact that there is at least one x for which x will work if and only if x is a cashier we can infer that there is at least one x for which if x were a cashier, then x is working via existential biconditional elimination. From the fact that for all x, x is a cashier if and only if x will work we can infer that for all x, if x works, then x is a cashier via universal biconditional elimination. Finally, from the fact that there is at least one x for which if x were a cashier, then x is working, and that for all x, if x works, then x is a cashier we can infer that there is at least one x for which x is a cashier if and only if x will work via existential biconditional introduction. Therefore, the answer is yes.