  Notice that D1 and D2 together entail that if the one is, then Purity-F is false. To see why, consider the following. D1 establishes that if Purity-F is true, then if the one is, then the one is neither F nor con-F; and D2 establishes that if the one is, then the one is both F and con-F. So if both D1 and D2 are valid and based on acceptable premises (other than Purity-F), then D1 and D2 together establish that if Purity-F is true and the one is, then the one has contradictory properties. Given that it is impossible for something to have contradictory properties, it is a direct consequence of the conjunction of D1 and D2 that if the one is, then Purity-F is false.