Consider the following premises. For all z, z is a scientist if and only if z will read a book. There is at least one z for which z will work if and only if z will read a book. 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 z works, then z is a scientist.
 From the fact that there is at least one z for which z will work if and only if z will read a book we can infer that there is at least one z for which if z works, then z is reading a book via existential biconditional elimination. From the fact that for all z, z is a scientist if and only if z will read a book we can infer that for all z, if z reads a book, then z is a scientist via universal biconditional elimination. Finally, from the fact that there is at least one z for which if z works, then z is reading a book, and that for all z, if z reads a book, then z is a scientist we can infer that there is at least one z for which if z works, then z is a scientist via existential transitivity. Therefore, the answer is yes.