Consider the following premises. For all x_10, if x_10 drinks water, then x_10 is a cashier. John is drinking water or John is not a cashier. Can we infer the following from them? If we can, name the inference rule being used: If is not true that John is a cashier if and only if John is drinking water.
 From the fact that for all x_10, if x_10 drinks water, then x_10 is a cashier we can infer that if John drinks water, then John is a cashier via universal instantiation. From the fact that John is drinking water or John is not a cashier we can infer that if John were a cashier, then John is drinking water via rewriting. Finally, from the fact that if John were a cashier, then John is drinking water, and that if John drinks water, then John is a cashier we can infer that John is a cashier if and only if John is drinking water via biconditional introduction, which contradicts that If is not true that John is a cashier if and only if John is drinking water. Therefore, the answer is no.