Towards the end of Civil War, Captain America:
Starts smashing up Iron Man's Arc Reactor.
Doesn't he need that to live?
Was Steve going for a kill shot, or did he not realise how important it was?
Tony hasn't needed the reactor to live ever since the end of Iron Man 3, when he underwent surgery to remove it. He doesn't wear it any more; now, the reactor is only for the suit.
[we see Tony undergoing surgery to remove the shrapnel near his heart]
Tony Stark: [voice over] Of course, there are people who say progress is dangerous. But I'll bet none of those idiots ever had to live with a chest full of shrapnel. And now...neither will I. Let me tell you, that was the best sleep I'd had in years.
It's likely Steve Rogers knew about this, since some time passed since Iron Man 3.
Once the shrapnel was removed iron man didn't need it to live but only for the suit to function so therefore once he destroyed the reactor the suit shut down.
Its more that Capt America knew he needed it to function rather than to live. With the reactor damaged, he could beat Iron Man.
I don't really think Cap knew that Tony removed the Arc Reactor. In the movie as you have seen, Cap does take a couple shots at the reactor which lead me to assume that Cap didn't know. And then again, Tony could have told Cap during the second Avengers movie. Also, reactor or not, Capt wouldn't have cared because when Tony started attacking Bucky, Cap just wanted to protect Bucky.
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