How do you know oxygen exists?

W/o, or too little oxygen you'd begin to feel a bit strange, pass out and eventually die.

As long as you don't, there's a fair chance that there is oxygen in the air.

Or light a candle. It'll flicker and go out if there's not enough oxygen.
beacus there is beacus there is Because if there wasn't, you wouldn't be breathing in the first place!