Consider the following premises. If Mary were a cashier, then it is windy. It is windy if and only if Mary is a cashier. If Mary were a cashier, then it is windy. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Mary is a cashier if and only if it is windy.
 From the fact that it is windy if and only if Mary is a cashier we can infer that if it is windy, then Mary is a cashier via biconditional elimination. Finally, from the fact that if Mary were a cashier, then it is windy, and that if it is windy, then Mary is a cashier we can infer that Mary is a cashier if and only if it is windy via biconditional introduction, which contradicts that If is not true that Mary is a cashier if and only if it is windy. Therefore, the answer is no.