Consider the following premises. It is snowing or Patricia is not a nurse. If it snows, then Patricia is a nurse. Patricia is a nurse. Can we infer the following from them? If we can, name the inference rule being used: It is not snowing.
 From the fact that it is snowing or Patricia is not a nurse we can infer that if Patricia were a nurse, then it is snowing via rewriting. From the fact that if it snows, then Patricia is a nurse, and that if Patricia were a nurse, then it is snowing we can infer that it is snowing if and only if Patricia is a nurse via biconditional introduction. From the fact that it is snowing if and only if Patricia is a nurse we can infer that if Patricia were a nurse, then it is snowing via biconditional elimination. Finally, from the fact that if Patricia were a nurse, then it is snowing, and that Patricia is a nurse we can infer that it is snowing via modus ponens, which contradicts that It is not snowing. Therefore, the answer is no.