# Existence of a function continuous everywhere and nowhere differentialable

We know there exists some functions, such that Weierstrass one, that are continuous everywhere on $$[0 ; 1]$$ and nowhere differentiable. Their expression (and a little bit of work) would yield a proof. However, I was wondering if we can just prove the existence of such a function, without finding it. I searched on the web and found nothing. Would some of you have a reference or a proof?