Consider the following premises. For all x_10, if x_10 were an office clerk, then x_10 is curious. There is at least one x_10 for which x_10 is an office clerk if and only if x_10 is curious. For all x_10, if x_10 were curious, then x_10 is an office clerk. Can we infer the following from them? There is at least one x_10 for which x_10 is curious if and only if x_10 is an office clerk.
 From the fact that for all x_10, if x_10 were curious, then x_10 is an office clerk, and that for all x_10, if x_10 were an office clerk, then x_10 is curious we can infer that for all x_10, x_10 is curious if and only if x_10 is an office clerk. From the fact that there is at least one x_10 for which x_10 is an office clerk if and only if x_10 is curious we can infer that there is at least one x_10 for which if x_10 were curious, then x_10 is an office clerk. From the fact that for all x_10, x_10 is curious if and only if x_10 is an office clerk we can infer that for all x_10, if x_10 were an office clerk, then x_10 is curious. Finally, from the fact that there is at least one x_10 for which if x_10 were curious, then x_10 is an office clerk, and that for all x_10, if x_10 were an office clerk, then x_10 is curious we can infer that there is at least one x_10 for which x_10 is curious if and only if x_10 is an office clerk. Therefore, the answer is yes.