Consider the following premises. For all x_5, x_5 is a soldier if and only if x_5 will read a book. For all x_5, if x_5 were a musician, then x_5 is a soldier. For all x_5, if x_5 reads a book, then x_5 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will read a book if and only if x_5 is a soldier.
 From the fact that for all x_5, if x_5 reads a book, then x_5 is a musician, and that for all x_5, if x_5 were a musician, then x_5 is a soldier we can infer that for all x_5, if x_5 reads a book, then x_5 is a soldier via universal transitivity. From the fact that for all x_5, x_5 is a soldier if and only if x_5 will read a book we can infer that for all x_5, if x_5 were a soldier, then x_5 is reading a book via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 reads a book, then x_5 is a soldier, and that for all x_5, if x_5 were a soldier, 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 soldier via universal biconditional introduction. Therefore, the answer is yes.