How to avoid overly extensive introduction of otherwise unnecessary preliminaries for a minor result? For my PhD thesis I have proven a minor result but with the help of a theory that is far apart from my actual subjects. 

To have my work self-contained up to a certain level and to make my proof understandable, I should introduce like one page of notions, which I will never use again. 

The result is quite different from others. But even if it was just a modification of a known result, I don't think the line 


  "... can be obtained by a modification of the proof of XYZ to our
  needs..."


is appropriate in a PhD thesis.

How should I proceed in such cases?
An appendix, if allowed by your university style/guidelines (and it usually is), is the best option. It strikes a balance between two legitimate concerns:


you want your thesis to be self-contained, and you want to showcase the work you've done (as well as convince others of your work's quality)
in the main text, it may make your message less clear and burden the reader's mind with new notations