Consider the following premises. For all x_2, x_2 is not rich. For all x_2, if x_2 plays tennis, then x_2 is rich. For all x_2, if x_2 were a poet, then x_2 is playing tennis. For all x_2, if x_2 were rich, then x_2 is a poet. Can we infer the following from them? There is at least one x_2 for which x_2 is a poet.
 From the fact that for all x_2, if x_2 were a poet, then x_2 is playing tennis, and that for all x_2, if x_2 plays tennis, then x_2 is rich we can infer that for all x_2, if x_2 were a poet, then x_2 is rich. From the fact that for all x_2, if x_2 were rich, then x_2 is a poet, and that for all x_2, if x_2 were a poet, then x_2 is rich we can infer that for all x_2, x_2 is rich if and only if x_2 is a poet. Finally, from the fact that for all x_2, x_2 is rich if and only if x_2 is a poet, and that for all x_2, x_2 is not rich we can infer that for all x_2, x_2 is not a poet, which contradicts that There is at least one x_2 for which x_2 is a poet. Therefore, the answer is no.