Suppose one wants to use a theorem that was published quite a long time ago (+80 years) in a paper that is using a terminology and notations that are very much out-dated (making the paper very hard to read). Is it okay if we want to reformulate the result as well as the proof in an article using a more modern language (of course giving credit to the original paper)?

Or, on the other hand, is it something one shouldn't put in a research paper, since it's not a new result ? What is the general policy for this kind of things ?