Consider the following premises. For all x_5, if x_5 plays tennis, then x_5 is poor. For all x_5, if x_5 were poor, then x_5 is a scientist. For all x_5, if x_5 were a scientist, then x_5 is working. For all x_5, if x_5 works, then x_5 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is poor if and only if x_5 is a scientist.
 From the fact that for all x_5, if x_5 were a scientist, then x_5 is working, and that for all x_5, if x_5 works, then x_5 is playing tennis we can infer that for all x_5, if x_5 were a scientist, then x_5 is playing tennis via universal transitivity. From the fact that for all x_5, if x_5 were a scientist, then x_5 is playing tennis, and that for all x_5, if x_5 plays tennis, then x_5 is poor we can infer that for all x_5, if x_5 were a scientist, then x_5 is poor via universal transitivity. Finally, from the fact that for all x_5, if x_5 were poor, then x_5 is a scientist, and that for all x_5, if x_5 were a scientist, then x_5 is poor we can infer that for all x_5, x_5 is poor if and only if x_5 is a scientist via universal biconditional introduction. Therefore, the answer is yes.