Consider the following premises. There is at least one x_9 for which x_9 is a cashier if and only if x_9 is a nurse. For all x_9, x_9 is a nurse or x_9 is a lawyer. For all x_9, if x_9 were a lawyer, then x_9 is writing a letter. For all x_9, if x_9 writes a letter, then x_9 is a cashier. Can we infer the following from them? There is at least one x_9 for which x_9 is a cashier.
 From the fact that there is at least one x_9 for which x_9 is a cashier if and only if x_9 is a nurse we can infer that there is at least one x_9 for which if x_9 were a nurse, then x_9 is a cashier. From the fact that for all x_9, if x_9 were a lawyer, then x_9 is writing a letter, and that for all x_9, if x_9 writes a letter, then x_9 is a cashier we can infer that for all x_9, if x_9 were a lawyer, then x_9 is a cashier. Finally, from the fact that there is at least one x_9 for which if x_9 were a nurse, then x_9 is a cashier, that for all x_9, if x_9 were a lawyer, then x_9 is a cashier, and that for all x_9, x_9 is a nurse or x_9 is a lawyer we can infer that there is at least one x_9 for which x_9 is a cashier. Therefore, the answer is yes.