Consider the following premises. There is at least one x_1 for which x_1 is a poet. For all x_1, x_1 will work or x_1 is not a poet. For all x_1, x_1 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 x_1 for which x_1 will read a book and x_1 will work.
 From the fact that for all x_1, x_1 will work or x_1 is not a poet we can infer that for all x_1, if x_1 were a poet, then x_1 is working via universal rewriting. From the fact that for all x_1, if x_1 were a poet, then x_1 is working, and that there is at least one x_1 for which x_1 is a poet we can infer that there is at least one x_1 for which x_1 will work via existential modus ponens. Finally, from the fact that for all x_1, x_1 will read a book, and that there is at least one x_1 for which x_1 will work we can infer that there is at least one x_1 for which x_1 will read a book and x_1 will work via existential conjunction. Therefore, the answer is yes.