Consider the following premises. For all x_3, x_3 is not poor. For all x_3, x_3 is a cashier if and only if x_3 is a politician. For all x_3, x_3 is poor if and only if x_3 is a cashier. 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 a politician.
 From the fact that for all x_3, x_3 is poor if and only if x_3 is a cashier, and that for all x_3, x_3 is not poor we can infer that for all x_3, x_3 is not a cashier via universal biconditional elimination. Finally, from the fact that for all x_3, x_3 is a cashier if and only if x_3 is a politician, and that for all x_3, x_3 is not a cashier we can infer that for all x_3, x_3 is not a politician via universal biconditional elimination, which contradicts that There is at least one x_3 for which x_3 is a politician. Therefore, the answer is no.