Consider the following premises. There is at least one x_6 for which if x_6 reads a book, then x_6 is poor. For all x_6, if x_6 were poor, then x_6 is playing tennis. For all x_6, if x_6 were a poet, then x_6 is reading a book. For all x_6, if x_6 plays tennis, then x_6 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if is not true that x_6 is a poet if and only if x_6 is poor.
 From the fact that for all x_6, if x_6 were a poet, then x_6 is reading a book, and that there is at least one x_6 for which if x_6 reads a book, then x_6 is poor we can infer that there is at least one x_6 for which if x_6 were a poet, then x_6 is poor via existential transitivity. From the fact that for all x_6, if x_6 were poor, then x_6 is playing tennis, and that for all x_6, if x_6 plays tennis, then x_6 is a poet we can infer that for all x_6, if x_6 were poor, then x_6 is a poet via universal transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 were a poet, then x_6 is poor, and that for all x_6, if x_6 were poor, then x_6 is a poet we can infer that there is at least one x_6 for which x_6 is a poet if and only if x_6 is poor via existential biconditional introduction, which contradicts that For all x_6, if is not true that x_6 is a poet if and only if x_6 is poor. Therefore, the answer is no.