The phrase "as I demonstrated" is correct and usable in written English.
You can use it when referring to a previous explanation or example you provided to illustrate a point.
Example: "The results of the experiment were consistent with my earlier findings, as I demonstrated in the previous section."
Alternatives: "as I showed" or "as I illustrated".
Being a mother and wife was satisfying as I demonstrated my love for my three children and their father.
But as I demonstrated last year, those free links don't produce nearly as many inquiries for me as AdWords does.
As I demonstrated in a study published last year, there were at least 56 attempts to employ the direct or indirect threat of mass migrations as a non-military instrument of influence between 1951 and 2006.
As I demonstrated on Friday, renewed and substantial negotiations must be sought now because the threats to Tibetan culture are real.
As I demonstrated above, certification induces a producer to improve the quality of his good when the certification standards exceed the producer's ideal (the area on and above the diagonal).
As I demonstrated a bath, there were a lot of smiles and chuckles in the room.
But, hey, we can take a joke, as I demonstrate in this Cartoon Lounge.
Still, within its recondite iambs, relevance can be found, as I demonstrate in this Cartoon Lounge episode.
As a result, we are about to hand over control of Britain's future energy policy and climate security to the French government – as I demonstrate with Charles Secrett, Tom Burker and Tony Juniper in a note to the prime minister today.
As I demonstrate in the latest issue of the journal Social Science History, by examining the changing frequencies of key words in books published in the United States, researchers can gain new perspectives on America and its novels.
As I demonstrate below, the main difference between the Piketty time series for UK inequality and the Giles time series for UK inequality, is that Piketty corrects his data series to allow for this 23 percentage-point drop (caused by changes in the methodology used to measure the wealth distribution), whereas Giles does not.
