The last complete, but unpublished, paper by the late Tom Etter titled "Three-Place Identity" purports to prove that all of mathematics can be expressed in terms of relative identity. In his own words from the abstract:
In this paper it will be shown that all of mathematics can be expressed in terms of relative identity when this concept is formalized as a three-place predicate. My focus here will be on the proof of this theorem, though I'll also take a brief look at how three-place identity might help to expand the horizons of science, which is the main topic of a longer paper, Membership and Identity.
He proceeds to do so by proving relative identity can express set theory.
Unfortunately, Etter was to pass away before completing the longer paper.
Is this result already known to mathematics -- perhaps under another name? If not, is the result is incorrect? If correct and not previously known, does it have broad implications, including for the philosophy of science?