Consider the following premises. For all x_11, if x_11 were rich, then x_11 is a soldier. There is at least one x_11 for which if x_11 were a soldier, then x_11 is rich. For all x_11, x_11 is a soldier if and only if x_11 is rich. Can we infer the following from them? There is at least one x_11 for which x_11 is rich if and only if x_11 is a soldier.
 From the fact that for all x_11, x_11 is a soldier if and only if x_11 is rich we can infer that for all x_11, if x_11 were rich, then x_11 is a soldier. From the fact that there is at least one x_11 for which if x_11 were a soldier, then x_11 is rich, and that for all x_11, if x_11 were rich, then x_11 is a soldier we can infer that there is at least one x_11 for which x_11 is a soldier if and only if x_11 is rich. From the fact that there is at least one x_11 for which x_11 is a soldier if and only if x_11 is rich we can infer that there is at least one x_11 for which if x_11 were a soldier, then x_11 is rich. Finally, from the fact that for all x_11, if x_11 were rich, then x_11 is a soldier, and that there is at least one x_11 for which if x_11 were a soldier, then x_11 is rich we can infer that there is at least one x_11 for which x_11 is rich if and only if x_11 is a soldier. Therefore, the answer is yes.