Consider the following premises. For all x_7, x_7 is a poet if and only if x_7 is an office clerk. For all x_7, if x_7 reads a book, then x_7 is a politician. For all x_7, if x_7 were a politician, then x_7 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, if x_7 reads a book, then x_7 is an office clerk.
 From the fact that for all x_7, x_7 is a poet if and only if x_7 is an office clerk we can infer that for all x_7, if x_7 were a poet, then x_7 is an office clerk via universal biconditional elimination. From the fact that for all x_7, if x_7 were a politician, then x_7 is a poet, and that for all x_7, if x_7 were a poet, then x_7 is an office clerk we can infer that for all x_7, if x_7 were a politician, then x_7 is an office clerk via universal transitivity. Finally, from the fact that for all x_7, if x_7 reads a book, then x_7 is a politician, and that for all x_7, if x_7 were a politician, then x_7 is an office clerk we can infer that for all x_7, if x_7 reads a book, then x_7 is an office clerk via universal transitivity. Therefore, the answer is yes.