Including proofs of known theorems in master's thesis
It would be a good idea to make it slightly more conspicuous that the theorem (and proof) are not original, e.g.:


  The following theorem is due to [5]; for the clarity of our exposition we give a more detailed version of the succinct proof in [5].


This leaves no doubt in the reader's mind that the work is not original, and also explains why you chose to include the proof.