About 2 months ago, I uploaded a fairly long paper (P1) to arXiv and it is currently under review.

Now, I am writing a second paper (P2) on a somewhat different topic. But quite unexpectedly, it seems that to justify a single small step in one section of (P2), I will need a result that I proved in (P1). Unfortunately, this result in (P1) needs several lemmas before it can be proved and the proof of it takes up about 5 pages in (P1).

I have two choices:

1. Do the small step in (P2) by merely citing the statement of the result from my recently uploaded arXiv paper (P1) : But as I mentioned before, the step for which I need this result is a rather small one. Would it really annoy the referee (eventually when I submit this paper) if he/she is referred to 5 pages in a long paper on arXiv merely to justify a small step?

Ideally, I would have liked to keep the papers disjoint, but it does not seem like I can get rid of this one small step in paper (P2).

2. Copy down the entire proof of the required result from (P1), probably in slightly abridged format. But even then, this is likely to add at least 3 pages to the current paper and so it feels unethical (like self plagiarism / salami slicing or something like that).

So what should I do? Are my worries about option 1 (annoying the referee) unfounded? If you were a referee, would you be irritated if I referred you to several pages in a long paper to justify one small step?

Thanks