Consider the following premises. For all x_13, if x_13 listens to a song, then x_13 is poor. For all x_13, x_13 is poor if and only if x_13 is a politician. For all x_13, x_13 will listen to a song if and only if x_13 is a politician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which the fact that x_13 were a politician does not imply that x_13 is poor.
 From the fact that for all x_13, x_13 will listen to a song if and only if x_13 is a politician we can infer that for all x_13, if x_13 were a politician, then x_13 is listening to a song via universal biconditional elimination. From the fact that for all x_13, if x_13 were a politician, then x_13 is listening to a song, and that for all x_13, if x_13 listens to a song, then x_13 is poor we can infer that for all x_13, if x_13 were a politician, then x_13 is poor via universal transitivity. From the fact that for all x_13, x_13 is poor if and only if x_13 is a politician we can infer that for all x_13, if x_13 were poor, then x_13 is a politician via universal biconditional elimination. From the fact that for all x_13, if x_13 were poor, then x_13 is a politician, and that for all x_13, if x_13 were a politician, then x_13 is poor we can infer that for all x_13, x_13 is poor if and only if x_13 is a politician via universal biconditional introduction. Finally, from the fact that for all x_13, x_13 is poor if and only if x_13 is a politician we can infer that for all x_13, if x_13 were a politician, then x_13 is poor via universal biconditional elimination, which contradicts that There is at least one x_13 for which the fact that x_13 were a politician does not imply that x_13 is poor. Therefore, the answer is no.