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How to do it:

Put down two bells and get in pushup position Do a pushup and a row. Be sure to
flare your lats and rip the weight off the floor.
With your arm at your side, immediately do a tricep kickback.
When starting this, use lower weights initially. I find that people who start this usually feel it in their core, either in the abs or along the front of the hip, so assume that the arms won't be much of an issue.

The ultimate version of this is called a five-in-one since it trains 5 movements at once. I have to admit that this is one of my all-time favorites. This consists of starting with your body stiff, then doing a
  1. front lever to tuck you up into a ball and immediately reversing it with a
  2. back lever followed by a
  3. pushup then a
  4. row as described here and a
  5. tricep kickback.
This looks at first glance like you are just hopping back and forth before performing the pushup. but if you really just post and use you shoulders and back to move you won't believe the amount of work you have just done. This accounts for their other nickname, asskickers. Note that you can and should abruptly change direction between the front and back levers to really work your upper body – landing on your feet should be just a touch with the floor rather than a full stop. This pretty much covers everything you can do with your chest, shoulders and back at once. And yes for the pushup you can do them one-armed, one-legged too.

Depending on how much weight you have and your back, you might have to arch. I confess I am overly arched in the picture because thanks to the slow shutter speed on the camera, I had to post for several seconds for each of the frames (try posting in the kickback and see if you back doesn't arch!) In any case, if you need to arch some that is fine.