Just don't worry about objectively proving that - instead, take it as axiomatic, and we'll be okay ;)
It all depends on your axioms, in the end. The devout Christian will tell you that hedonism is wrong because God says so. And despite a lot of noise otherwise, the objectivist answer really boils down to not much more than saying that hedonism is wrong because Rand says so. The casual reader may be excused for failing to see how the second is an objective improvement over the first...
No, I won't attempt to prove liberty's absoluteness. I'll simply do what all else do, and ask that they make the case against it. Argue that all societies based on it's negation failed, or are in the process of failing. That people aren't drawn to slavery.
I'll also challenge others to add other moral absolutes that can stand as axioms with liberty. I currently know of none. Liberty is inherent in the human condition -- again something I assert, not something I propose to prove.