Consider the following premises. For all z_2, z_2 is a writer or z_2 is a janitor. For all z_2, if z_2 were a janitor, then z_2 is working. For all z_2, z_2 will work or z_2 is not a writer. There is at least one z_2 for which z_2 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_2 for which z_2 will work and z_2 will write a letter.
 From the fact that for all z_2, z_2 will work or z_2 is not a writer we can infer that for all z_2, if z_2 were a writer, then z_2 is working via universal rewriting. From the fact that for all z_2, if z_2 were a writer, then z_2 is working, that for all z_2, if z_2 were a janitor, then z_2 is working, and that for all z_2, z_2 is a writer or z_2 is a janitor we can infer that for all z_2, z_2 will work via universal disjunction elimination. Finally, from the fact that for all z_2, z_2 will work, and that there is at least one z_2 for which z_2 will write a letter we can infer that there is at least one z_2 for which z_2 will work and z_2 will write a letter via existential conjunction. Therefore, the answer is yes.