Consider the following premises. For all z_1, z_1 is happy if and only if z_1 is a writer. For all z_1, if z_1 were a writer, then z_1 is happy. There is at least one z_1 for which z_1 is not a writer. 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 happy.
 From the fact that for all z_1, z_1 is happy if and only if z_1 is a writer we can infer that for all z_1, if z_1 were happy, then z_1 is a writer via universal biconditional elimination. From the fact that for all z_1, if z_1 were happy, then z_1 is a writer, and that for all z_1, if z_1 were a writer, then z_1 is happy we can infer that for all z_1, z_1 is happy if and only if z_1 is a writer via universal biconditional introduction. Finally, from the fact that for all z_1, z_1 is happy if and only if z_1 is a writer, and that there is at least one z_1 for which z_1 is not a writer we can infer that there is at least one z_1 for which z_1 is not happy via existential biconditional elimination. Therefore, the answer is yes.