What to do when you have small yet additional results to a submitted paper?
As Marc says in his comment, the best thing to do is probably to incorporate the new proof into your revision, after you get reviewer feedback. A small extension not worth its own paper is unlikely to make a difference between reject and revise. If you send it now, it may annoy the editor and reviewers. Also, the reviewers will likely be just fine with more new material you add in revision.