[Epa095]

I dont really know what you mean by truth-preserving here, but maybe a hint is thats its not ONLY subtraction which is functionally complete, it's subtraction and the constant symbol 0. From subtraction and 0 he makes false (as -0.0), and then he has the functionally complete set found in wikipedia [1] as {->, _|_ } (my attempt at rendering rightarrow and bottom).

1: https://en.wikipedia.org/wiki/Functional_completeness

[Joker_vD]

Truth-preserving means that it maps T to T. In fact, the Wikipedia's article you link to has Post's theorem about five Post's classes of Boolean functions with all of their definitions: monotonic, affine (which has a funny definition in this article: I was taught the definiton via ANF, "is just a XOR of (some) of variables"), self-dual, truth- and false-preserving. They're all closed but functionally incomplete (in fact, they're functionally pre-complete: adding any single function outside of a class to that class produces a functionally complete set, — and there are no other pre-complete classes).