Consider the following premises. For all x_7, x_7 will take a plane if and only if x_7 will read a book. For all x_7, if x_7 were a scientist, then x_7 is reading a book. There is at least one x_7 for which x_7 will not take a plane. For all x_7, if x_7 reads a book, then x_7 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not a scientist.
 From the fact that for all x_7, x_7 will take a plane if and only if x_7 will read a book, and that there is at least one x_7 for which x_7 will not take a plane we can infer that there is at least one x_7 for which x_7 will not read a book via existential biconditional elimination. From the fact that for all x_7, if x_7 were a scientist, then x_7 is reading a book, and that for all x_7, if x_7 reads a book, then x_7 is a scientist we can infer that for all x_7, x_7 is a scientist if and only if x_7 will read a book via universal biconditional introduction. Finally, from the fact that for all x_7, x_7 is a scientist if and only if x_7 will read a book, and that there is at least one x_7 for which x_7 will not read a book we can infer that there is at least one x_7 for which x_7 is not a scientist via existential biconditional elimination. Therefore, the answer is yes.