Sign of Difference between Prime-Counting Function and Eulerian Logarithmic Integral Changes Infinitely Often

Theorem
Let $\pi \left({n}\right)$ denote the prime-counting function.

The sign of $\pi \left({n}\right) - \displaystyle \int_2^n \frac {\mathrm d x} {\ln x}$ changes infinitely often as $n$ increases indefinitely.