Consider the following premises. If it is cold, then Patricia is a nurse. If Elisabeth were fast, then it is cold. If Patricia were a nurse, then Elisabeth is fast. If it is cold, then Patricia is a nurse. Can we infer the following from them? If we can, name the inference rule being used: If is not true that it is cold if and only if Patricia is a nurse.
 From the fact that if Patricia were a nurse, then Elisabeth is fast, and that if Elisabeth were fast, then it is cold we can infer that if Patricia were a nurse, then it is cold via transitivity. Finally, from the fact that if it is cold, then Patricia is a nurse, and that if Patricia were a nurse, then it is cold we can infer that it is cold if and only if Patricia is a nurse via biconditional introduction, which contradicts that If is not true that it is cold if and only if Patricia is a nurse. Therefore, the answer is no.