Consider the following premises. For all z_3, if z_3 writes a letter, then z_3 is making tea. There is at least one z_3 for which if z_3 writes a letter, then z_3 is working. For all z_3, z_3 will not make tea. For all z_3, if z_3 works, then z_3 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_3 for which z_3 will not work.
 From the fact that for all z_3, if z_3 writes a letter, then z_3 is making tea, and that for all z_3, z_3 will not make tea we can infer that for all z_3, z_3 will not write a letter via universal modus tollens. From the fact that for all z_3, if z_3 works, then z_3 is writing a letter, and that there is at least one z_3 for which if z_3 writes a letter, then z_3 is working we can infer that there is at least one z_3 for which z_3 will work if and only if z_3 will write a letter via existential biconditional introduction. Finally, from the fact that there is at least one z_3 for which z_3 will work if and only if z_3 will write a letter, and that for all z_3, z_3 will not write a letter we can infer that there is at least one z_3 for which z_3 will not work via existential biconditional elimination. Therefore, the answer is yes.