Consider the following premises. For all x_10, if x_10 were rich, then x_10 is playing tennis. For all x_10, x_10 is curious if and only if x_10 is rich. There is at least one x_10 for which if x_10 plays tennis, then x_10 is curious. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which if x_10 were rich, then x_10 is playing tennis.
 From the fact that for all x_10, x_10 is curious if and only if x_10 is rich we can infer that for all x_10, if x_10 were curious, then x_10 is rich via universal biconditional elimination. From the fact that there is at least one x_10 for which if x_10 plays tennis, then x_10 is curious, and that for all x_10, if x_10 were curious, then x_10 is rich we can infer that there is at least one x_10 for which if x_10 plays tennis, then x_10 is rich via existential transitivity. From the fact that there is at least one x_10 for which if x_10 plays tennis, then x_10 is rich, and that for all x_10, if x_10 were rich, then x_10 is playing tennis we can infer that there is at least one x_10 for which x_10 will play tennis if and only if x_10 is rich via existential biconditional introduction. Finally, from the fact that there is at least one x_10 for which x_10 will play tennis if and only if x_10 is rich we can infer that there is at least one x_10 for which if x_10 were rich, then x_10 is playing tennis via existential biconditional elimination. Therefore, the answer is yes.