Consider the following premises. There is at least one y_3 for which if y_3 were a soldier, then y_3 is a cashier. For all y_3, y_3 is a cashier if and only if y_3 is a soldier. Can we infer the following from them? For all y_3, the fact that y_3 were a cashier does not imply that y_3 is a soldier.
That contradicts the premises. Therefore the answer is no.