Consider the following premises. For all x_7, if x_7 reads a book, then x_7 is a writer. For all x_7, x_7 is a politician or x_7 is not a writer. For all x_7, if x_7 were a writer, then x_7 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which the fact that x_7 reads a book does not imply that x_7 is a politician.
 From the fact that for all x_7, x_7 is a politician or x_7 is not a writer we can infer that for all x_7, if x_7 were a writer, then x_7 is a politician via universal rewriting. From the fact that for all x_7, if x_7 reads a book, then x_7 is a writer, and that for all x_7, if x_7 were a writer, then x_7 is reading a book we can infer that for all x_7, x_7 will read a book if and only if x_7 is a writer via universal biconditional introduction. From the fact that for all x_7, x_7 will read a book if and only if x_7 is a writer we can infer that for all x_7, if x_7 reads a book, then x_7 is a writer via universal biconditional elimination. Finally, from the fact that for all x_7, if x_7 reads a book, then x_7 is a writer, and that for all x_7, if x_7 were a writer, then x_7 is a politician we can infer that for all x_7, if x_7 reads a book, then x_7 is a politician via universal transitivity, which contradicts that There is at least one x_7 for which the fact that x_7 reads a book does not imply that x_7 is a politician. Therefore, the answer is no.