Consider the following premises. For all z, z will read a book and z is an artist. For all x_2, x_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 x_2 for which x_2 will write a letter and x_2 will read a book.
 From the fact that for all z, z will read a book and z is an artist we can infer that for all z, z will read a book via universal simplification. From the fact that for all z, z will read a book we can infer that Michael is reading a book via universal instantiation. From the fact that Michael is reading a book we can infer that there is at least one x_2 for which x_2 will read a book via existential generalization. Finally, from the fact that for all x_2, x_2 will write a letter, and that there is at least one x_2 for which x_2 will read a book we can infer that there is at least one x_2 for which x_2 will write a letter and x_2 will read a book via existential conjunction. Therefore, the answer is yes.