Consider the following premises. For all x_6, if x_6 were sad, then x_6 is poor. For all x_6, if x_6 were a cashier, then x_6 is sad. For all x_6, x_6 is a cashier or x_6 is not poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is a cashier if and only if x_6 is sad.
 From the fact that for all x_6, x_6 is a cashier or x_6 is not poor we can infer that for all x_6, if x_6 were poor, then x_6 is a cashier via universal rewriting. From the fact that for all x_6, if x_6 were sad, then x_6 is poor, and that for all x_6, if x_6 were poor, then x_6 is a cashier we can infer that for all x_6, if x_6 were sad, then x_6 is a cashier via universal transitivity. Finally, from the fact that for all x_6, if x_6 were a cashier, then x_6 is sad, and that for all x_6, if x_6 were sad, then x_6 is a cashier we can infer that for all x_6, x_6 is a cashier if and only if x_6 is sad via universal biconditional introduction. Therefore, the answer is yes.