I doubt very much that this has been "proven". Scott Lilienfeld has said, to paraphrase that "what's new about EMDR doesn't work" and what works isn't new". Basically, EMDR is good old exposure therapy, which has been proven, with a bunch of eye twitching tossed in for variety. This latter has not been shown to be a useful addition.
This. I have a friend who's researched it extensively, and has found that "evidence" for EMDR is very weak, and its use is often associated with psychological therapies that are actually harmful.