Consider the following premises. For all x, if x were a nurse, then x is reading a book. John is a nurse if and only if it is sunny. For all x, x will not read a book. For all x, if x reads a book, then x is a nurse. Can we infer the following from them? If we can, name the inference rule being used: It is not sunny.
 From the fact that for all x, if x were a nurse, then x is reading a book, and that for all x, if x reads a book, then x is a nurse we can infer that for all x, x is a nurse if and only if x will read a book via universal biconditional introduction. From the fact that for all x, x is a nurse if and only if x will read a book, and that for all x, x will not read a book we can infer that for all x, x is not a nurse via universal biconditional elimination. From the fact that for all x, x is not a nurse we can infer that John is not a nurse via universal instantiation. Finally, from the fact that John is a nurse if and only if it is sunny, and that John is not a nurse we can infer that it is not sunny via biconditional elimination. Therefore, the answer is yes.