I would have to agree that FC2 did this first. Since then Crysis 2 and CoDBlOps have also done it (I don't recall the dive to prone in Battlefield 3, but it was entertaining in what little BlOps I played).
This shooting over cover (popularised by Red Orchestra 2?) I first saw in Call of Juarez: Bound by Blood (or whatever it was called.. It was the second one). I've since seen it in Crysis 2 and now Far Cry 3 (and kudos to Red Orchestra 2 for having it in multiplayer I assume). When my friends and I first saw this mechanic, we agreed that it should be standard in all future FPS's. Why should 3rd person 'cover shooters' get all the good cover mechanics?
Combine the two and we could have sliding to cover in our FPS games. (Well, I mentioned Crysis 2 in both of those examples, so I guess there's that. Crysis 3 should have the same movement mechanics.)