Consider the following premises. For all x_5, if x_5 were a politician, then x_5 is reading a book. For all x_5, if x_5 reads a book, then x_5 is a politician. There is at least one x_5 for which x_5 is a politician or x_5 is a cashier. For all x_5, x_5 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not a cashier.
 From the fact that for all x_5, if x_5 reads a book, then x_5 is a politician, and that for all x_5, if x_5 were a politician, then x_5 is reading a book we can infer that for all x_5, x_5 will read a book if and only if x_5 is a politician via universal biconditional introduction. From the fact that for all x_5, x_5 will read a book if and only if x_5 is a politician, and that for all x_5, x_5 will not read a book we can infer that for all x_5, x_5 is not a politician via universal biconditional elimination. Finally, from the fact that there is at least one x_5 for which x_5 is a politician or x_5 is a cashier, and that for all x_5, x_5 is not a politician we can infer that there is at least one x_5 for which x_5 is a cashier via existential disjunctive syllogism, which contradicts that For all x_5, x_5 is not a cashier. Therefore, the answer is no.