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