Consider the following premises. For all x_4, x_4 is excited if and only if x_4 is a cashier. There is at least one x_4 for which x_4 is a cashier. Can we infer the following from them? There is at least one x_4 for which x_4 is excited.
 From the fact that for all x_4, x_4 is excited if and only if x_4 is a cashier we can infer that for all x_4, if x_4 were a cashier, then x_4 is excited. Finally, from the fact that for all x_4, if x_4 were a cashier, then x_4 is excited, and that there is at least one x_4 for which x_4 is a cashier we can infer that there is at least one x_4 for which x_4 is excited. Therefore, the answer is yes.