Not sure if that's an application as much as a tautology

It's a proof, so sure it's a tautology.

Here's a better way of masking it though: suppose we believe:

1. We should be non-sadistic: X < 0 ==> X+Y < Y
2. Accepting of dominance: X > 0 ==> X+Y > Y

This is exactly what it means to be order preserving, but maybe when phrased this way the result seems more surprising (in the sense that those axioms are harder to refute)?