Consider the following premises. For all x, x is fast if and only if x is a nurse. There is at least one x for which if x were fast, then x is a nurse. For all x, x is a nurse if and only if x is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x, if is not true that x is fast if and only if x is a nurse.
That contradicts the premises. Therefore the answer is no.