Consider the following premises. John is a nurse if and only if it is late. Richard is not climbing a mountain. For all x_7, x_7 is a police officer if and only if x_7 is a nurse. Richard is climbing a mountain if and only if it is late. Can we infer the following from them? If we can, name the inference rule being used: John is a police officer.
 From the fact that Richard is climbing a mountain if and only if it is late, and that Richard is not climbing a mountain we can infer that it is not late via biconditional elimination. From the fact that for all x_7, x_7 is a police officer if and only if x_7 is a nurse we can infer that John is a police officer if and only if John is a nurse via universal instantiation. From the fact that John is a nurse if and only if it is late, and that it is not late we can infer that John is not a nurse via biconditional elimination. Finally, from the fact that John is a police officer if and only if John is a nurse, and that John is not a nurse we can infer that John is not a police officer via biconditional elimination, which contradicts that John is a police officer. Therefore, the answer is no.