Consider the following premises. If Barbara were a nurse, then Barbara is working. If it is windy, then Patricia is rich. If it snows, then it is windy. If Barbara works, then it is snowing. Can we infer the following from them? If we can, name the inference rule being used: The fact that Barbara were a nurse does not imply that Patricia is rich.
 From the fact that if Barbara works, then it is snowing, and that if it snows, then it is windy we can infer that if Barbara works, then it is windy via transitivity. From the fact that if Barbara works, then it is windy, and that if it is windy, then Patricia is rich we can infer that if Barbara works, then Patricia is rich via transitivity. Finally, from the fact that if Barbara were a nurse, then Barbara is working, and that if Barbara works, then Patricia is rich we can infer that if Barbara were a nurse, then Patricia is rich via transitivity, which contradicts that The fact that Barbara were a nurse does not imply that Patricia is rich. Therefore, the answer is no.