As usual, you've accidentally stumbled halfway into a true statement.
Science doesn't "prove" much, but it is exceptionally good as disproving things. It's far more useful at proving what cannot be instead of what is. Think of it as a process of elimination.
"Once you eliminate the impossible, whatever remains, however improbable, must be the truth." -- Sherlock Holmes.
So while science cannot prove you breathe air, as opposed to, say, absorbing oxygen through osmosis, we can attempt to rule that out as a possibility.
The experiment is quite simple: Stop breathing, and we'll observe what happens next.
Personally, my theory is that you'll turn blue, pass out, and barring any outside intervention, suffer brain damage and eventually die from hypoxia. But hey, maybe "science" is wrong, hmmm AV?