Consider the following premises. Thomas is curious if and only if Michael is sad. Thomas is curious if and only if Robert is a police officer. Robert is not a police officer. For all x_7, x_7 is sad if and only if x_7 will read a book. Can we infer the following from them? If we can, name the inference rule being used: Michael is not reading a book.
 From the fact that Thomas is curious if and only if Robert is a police officer, and that Robert is not a police officer we can infer that Thomas is not curious via biconditional elimination. From the fact that for all x_7, x_7 is sad if and only if x_7 will read a book we can infer that Michael is sad if and only if Michael is reading a book via universal instantiation. From the fact that Thomas is curious if and only if Michael is sad, and that Thomas is not curious we can infer that Michael is not sad via biconditional elimination. Finally, from the fact that Michael is sad if and only if Michael is reading a book, and that Michael is not sad we can infer that Michael is not reading a book via biconditional elimination. Therefore, the answer is yes.