Consider the following premises. For all x_7, if x_7 reads a book, then x_7 is a nurse. There is at least one x_7 for which x_7 is a taxi driver or x_7 will read a book. For all x_7, if x_7 were a nurse, then x_7 is an astronaut. For all x_7, x_7 is a taxi driver if and only if x_7 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not an astronaut.
 From the fact that for all x_7, x_7 is a taxi driver if and only if x_7 is an astronaut we can infer that for all x_7, if x_7 were a taxi driver, then x_7 is an astronaut via universal biconditional elimination. From the fact that for all x_7, if x_7 reads a book, then x_7 is a nurse, and that for all x_7, if x_7 were a nurse, then x_7 is an astronaut we can infer that for all x_7, if x_7 reads a book, then x_7 is an astronaut via universal transitivity. Finally, from the fact that for all x_7, if x_7 were a taxi driver, then x_7 is an astronaut, that for all x_7, if x_7 reads a book, then x_7 is an astronaut, and that there is at least one x_7 for which x_7 is a taxi driver or x_7 will read a book we can infer that there is at least one x_7 for which x_7 is an astronaut via existential disjunction elimination, which contradicts that For all x_7, x_7 is not an astronaut. Therefore, the answer is no.