Consider the following premises. For all x_1, if x_1 were happy, then x_1 is reading a book. For all x_1, if x_1 reads a book, then x_1 is happy. For all x_1, x_1 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 is happy.
 From the fact that for all x_1, if x_1 reads a book, then x_1 is happy, and that for all x_1, if x_1 were happy, then x_1 is reading a book we can infer that for all x_1, x_1 will read a book if and only if x_1 is happy via universal biconditional introduction. Finally, from the fact that for all x_1, x_1 will read a book if and only if x_1 is happy, and that for all x_1, x_1 will not read a book we can infer that for all x_1, x_1 is not happy via universal biconditional elimination, which contradicts that There is at least one x_1 for which x_1 is happy. Therefore, the answer is no.