Consider the following premises. For all x_1, if x_1 goes running, then x_1 is a politician. For all x_1, if x_1 were a politician, then x_1 is an astronaut. For all x_1, if x_1 were an astronaut, then x_1 is running. Can we infer the following from them? For all x_1, x_1 is a politician if and only if x_1 is an astronaut.
 From the fact that for all x_1, if x_1 were an astronaut, then x_1 is running, and that for all x_1, if x_1 goes running, then x_1 is a politician we can infer that for all x_1, if x_1 were an astronaut, then x_1 is a politician. Finally, from the fact that for all x_1, if x_1 were a politician, then x_1 is an astronaut, and that for all x_1, if x_1 were an astronaut, then x_1 is a politician we can infer that for all x_1, x_1 is a politician if and only if x_1 is an astronaut. Therefore, the answer is yes.