Consider the following premises. Linda is rich if and only if it is late. For all z, z is rich if and only if z will climb a mountain. For all z, z will not climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that for all z, z is rich if and only if z will climb a mountain, and that for all z, z will not climb a mountain we can infer that for all z, z is not rich via universal biconditional elimination. From the fact that for all z, z is not rich we can infer that Linda is not rich via universal instantiation. Finally, from the fact that Linda is rich if and only if it is late, and that Linda is not rich we can infer that it is not late via biconditional elimination, which contradicts that It is late. Therefore, the answer is no.