Consider the following premises. For all x_2, if x_2 reads a book, then x_2 is an office clerk. For all x_2, x_2 is an office clerk if and only if x_2 will read a book. For all x_2, if x_2 were an office clerk, then x_2 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_2 for which the fact that x_2 reads a book does not imply that x_2 is an office clerk.
 From the fact that for all x_2, if x_2 reads a book, then x_2 is an office clerk, and that for all x_2, if x_2 were an office clerk, then x_2 is reading a book we can infer that for all x_2, x_2 will read a book if and only if x_2 is an office clerk via universal biconditional introduction. From the fact that for all x_2, x_2 is an office clerk if and only if x_2 will read a book we can infer that for all x_2, if x_2 were an office clerk, then x_2 is reading a book via universal biconditional elimination. From the fact that for all x_2, x_2 will read a book if and only if x_2 is an office clerk we can infer that for all x_2, if x_2 reads a book, then x_2 is an office clerk via universal biconditional elimination. From the fact that for all x_2, if x_2 were an office clerk, then x_2 is reading a book, and that for all x_2, if x_2 reads a book, then x_2 is an office clerk we can infer that for all x_2, x_2 is an office clerk if and only if x_2 will read a book via universal biconditional introduction. Finally, from the fact that for all x_2, x_2 is an office clerk if and only if x_2 will read a book we can infer that for all x_2, if x_2 reads a book, then x_2 is an office clerk via universal biconditional elimination, which contradicts that There is at least one x_2 for which the fact that x_2 reads a book does not imply that x_2 is an office clerk. Therefore, the answer is no.