How do I cite a result that I've only seen stated without a proof, and I prove myself? I am writing my PhD thesis in mathematics.

It happens frequently that I use results that I don't have a reference for except


textbooks stating "it is easily seen that ..." or "it is well-known that..."
it is stated on Wikipedia (without proof)
I have derived it with colleagues or people from Q&amp;A sites


Then I try to find a source for some time, before I write down a proof by myself. However, most probably, there has been an earlier mention of this result that I could  reference instead.  

How should I proceed in such cases?
If it's a textbook-level result, you could just cite a textbook. Otherwise, if you derived it yourself or with colleagues, no citation is required unless you published that proof earlier (not likely if it's a minor one). But you should definitely thank the people who helped in acknowledgments.

Finally, note that there is a threshold for citation: if a result is trivial, and as such is likely to have been independently demonstrated by many people over time, with no clear historical/seminal work, then you do not need to cite it.