  So we can redescribe the Conclusion of D4 as follows: If Purity-F is true, then if the one is, then the others do not have a host of contrary properties. This means that D3 and D4 together entail that if the one is, then Purity-F is false. For, by D3, if the one is, then the others are both F and con-F. But, by D4, if Purity-F is true and the one is, then the others are neither F nor con-F. So, if Purity-F is true and the one is, then the others have a host of contradictory properties. Given that it is impossible for anything to have contradictory properties, it follows directly that if the one is, then Purity-F is false.