Consider the following premises. For all x_3, x_3 is sad if and only if x_3 is rich. There is at least one x_3 for which x_3 is rich if and only if x_3 is sad. Can we infer the following from them? There is at least one x_3 for which x_3 is sad if and only if x_3 is rich.
 From the fact that there is at least one x_3 for which x_3 is rich if and only if x_3 is sad we can infer that there is at least one x_3 for which if x_3 were rich, then x_3 is sad. From the fact that for all x_3, x_3 is sad if and only if x_3 is rich we can infer that for all x_3, if x_3 were sad, then x_3 is rich. Finally, from the fact that for all x_3, if x_3 were sad, then x_3 is rich, and that there is at least one x_3 for which if x_3 were rich, then x_3 is sad we can infer that there is at least one x_3 for which x_3 is sad if and only if x_3 is rich. Therefore, the answer is yes.