Consider the following premises. Charles is not a nurse. It is sunny. Charles is happy if and only if it is cold. For all x_16, x_16 is happy if and only if x_16 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: It is not cold and it is sunny.
 From the fact that for all x_16, x_16 is happy if and only if x_16 is a nurse we can infer that Charles is happy if and only if Charles is a nurse via universal instantiation. From the fact that Charles is happy if and only if Charles is a nurse, and that Charles is not a nurse we can infer that Charles is not happy via biconditional elimination. From the fact that Charles is happy if and only if it is cold, and that Charles is not happy we can infer that it is not cold via biconditional elimination. Finally, from the fact that it is not cold, and that it is sunny we can infer that it is not cold and it is sunny via conjunction. Therefore, the answer is yes.