Consider the following premises. For all x_2, x_2 is a mechanic if and only if x_2 will read a book. Can we infer the following from them? If we can, name the inference rule being used: If David were a mechanic, then David is reading a book.
 From the fact that for all x_2, x_2 is a mechanic if and only if x_2 will read a book we can infer that David is a mechanic if and only if David is reading a book via universal instantiation. Finally, from the fact that David is a mechanic if and only if David is reading a book we can infer that if David were a mechanic, then David is reading a book via biconditional elimination. Therefore, the answer is yes.