Consider the following premises. There is at least one x_6 for which if x_6 reads a book, then x_6 is happy. For all x_6, if x_6 reads a book, then x_6 is happy. For all x_6, if x_6 were happy, then x_6 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_6 for which x_6 is happy if and only if x_6 will read a book.
 From the fact that there is at least one x_6 for which if x_6 reads a book, then x_6 is happy, and that for all x_6, if x_6 were happy, then x_6 is reading a book we can infer that there is at least one x_6 for which x_6 will read a book if and only if x_6 is happy via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 will read a book if and only if x_6 is happy we can infer that there is at least one x_6 for which if x_6 were happy, then x_6 is reading a book via existential biconditional elimination. Finally, from the fact that there is at least one x_6 for which if x_6 were happy, then x_6 is reading a book, and that for all x_6, if x_6 reads a book, then x_6 is happy we can infer that there is at least one x_6 for which x_6 is happy if and only if x_6 will read a book via existential biconditional introduction. Therefore, the answer is yes.