The domain of your claim was "in any universe, under any set of assumptions". I now take it that you assume (see what I did there?) that all universes are sound according to classical logic and can admit no contradictions. You might be interested in <https://plato.stanford.edu/entries/impossible-worlds>, an overview of philosophical thinking on that subject.

Separately, if you scrub "plus rules like modus ponens" from my previous comment, do you agree with the rest of it?