Why is $M(x)=\frac{1}{x}\sum_{n\leq x}\mu(n)=o(1)$ ($x\to\infty$) equivalent to the Prime Number Theorem

Question

Where $\mu$ is the mobius function and $o(\phi)$ is a Lindau Symbol, $f=o(\phi)$ if and only if $f/\phi\to 0$.

Found it stated as an obvious fact in a math journal. I'd like a hint if it really is obvious or a proof if it's something well-known but rather difficult to show.