No-one has quite answered:
- When accepting without checking, how do you phrase it?
I think? So, here's a thought. I'm always of the opinion that you should give the maximal amount of detail where referencing something. Give the exact Theorem number in the paper you reference (not just ``by results of  it follows that...''). Explain carefully the hypotheses and conclusions. Of course, the more accepted a result is, the less detail you need to give.
If, however, you actually want to reference the proof then I'd be very careful. E.g. you might observe that the paper shows X=>Y, but the proof works for the weaker X'. I'd be tempted to give a sketch, or outline exactly the changes needed.
My guess is that a lot of subtle errors can be introduced by referencing proofs: I've heard it said that most mathematical results are true, but many proofs are subtly wrong. So it might be true that the proof in  shows that X'=>Y, but maybe the author stated it only for X because there is a subtle error in the proof, and really the stronger X is required. (This, of course, is also a good test of your own proofs, but I'm heading off topic...)