The instrumental convergence hypo-thesis, from the original paper[0] is this:
"Several instrumental values can be identified which are convergent in the sense that their attainment would increase the chances of the agent’s goal being realized for a wide range of final goals and a wide range of situations, implying that these instrumental values are likely to be pursued by many intelligent agents."
That's it, it is not at all formal and there's no proof provided for it, nor consistent evidence that it is true, and there are many contradictory possibilities suggested from nature and logic.
Its just something that's taken as given among the old guard pseudo-scientific quarters of the alignment "research" community.
[0] Bostrom's "The Superintelligent Will", the philosophy paper where he defines it: https://nickbostrom.com/superintelligentwill.pdf
EDIT: typos