Consider the following premises. For all x_8, if x_8 climbs a mountain, then x_8 is a nurse. David is a nurse if and only if Michael is making tea. For all x_8, if x_8 were a nurse, then x_8 is climbing a mountain. Michael is not making tea. Can we infer the following from them? If we can, name the inference rule being used: David is climbing a mountain.
 From the fact that for all x_8, if x_8 were a nurse, then x_8 is climbing a mountain, and that for all x_8, if x_8 climbs a mountain, then x_8 is a nurse we can infer that for all x_8, x_8 is a nurse if and only if x_8 will climb a mountain via universal biconditional introduction. From the fact that for all x_8, x_8 is a nurse if and only if x_8 will climb a mountain we can infer that David is a nurse if and only if David is climbing a mountain via universal instantiation. From the fact that David is a nurse if and only if Michael is making tea, and that Michael is not making tea we can infer that David is not a nurse via biconditional elimination. Finally, from the fact that David is a nurse if and only if David is climbing a mountain, and that David is not a nurse we can infer that David is not climbing a mountain via biconditional elimination, which contradicts that David is climbing a mountain. Therefore, the answer is no.