Consider the following premises. There is at least one z_1 for which z_1 is a politician if and only if z_1 is a scientist. For all z_1, z_1 will listen to a song. For all z_1, if z_1 were a scientist, then z_1 is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_1 for which z_1 is not a politician.
 From the fact that for all z_1, if z_1 were a scientist, then z_1 is not listening to a song, and that for all z_1, z_1 will listen to a song we can infer that for all z_1, z_1 is not a scientist via universal modus tollens. Finally, from the fact that there is at least one z_1 for which z_1 is a politician if and only if z_1 is a scientist, and that for all z_1, z_1 is not a scientist we can infer that there is at least one z_1 for which z_1 is not a politician via existential biconditional elimination. Therefore, the answer is yes.