Consider the following premises. There is at least one x_7 for which x_7 is a scientist if and only if x_7 is a politician. For all x_7, x_7 will read a book or x_7 is not a politician. For all x_7, x_7 will not read a book. For all x_7, if x_7 reads a book, then x_7 is a politician. 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 x_7 is not a scientist.
 From the fact that for all x_7, x_7 will read a book or x_7 is not a politician we can infer that for all x_7, if x_7 were a politician, then x_7 is reading a book via universal rewriting. 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 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 politician 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 politician, and that for all x_7, x_7 will not read a book we can infer that for all x_7, x_7 is not a politician via universal biconditional elimination. Finally, from the fact that there is at least one x_7 for which x_7 is a scientist if and only if x_7 is a politician, and that for all x_7, x_7 is not a politician we can infer that there is at least one x_7 for which x_7 is not a scientist via existential biconditional elimination. Therefore, the answer is yes.