Consider the following premises. There is at least one z_2 for which z_2 will make tea. For all z_2, z_2 will read a book. 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 read a book.
 From the fact that for all z_2, z_2 will read a book, and that there is at least one z_2 for which z_2 will make tea we can infer that there is at least one z_2 for which z_2 will read a book and z_2 will make tea via existential conjunction. Finally, from the fact that there is at least one z_2 for which z_2 will read a book and z_2 will make tea we can infer that there is at least one z_2 for which z_2 will read a book via existential simplification. Therefore, the answer is yes.