Point at which Prime-Counting Function becomes less than Eulerian Logarithmic Integral/Using Riemann Hypothesis

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

Let $a \uparrow b$ be interpreted as Knuth notation for $a^b$.

Suppose the Riemann Hypothesis holds.

Then:
 * $\exists n < 10 \uparrow \left({10 \uparrow \left({10 \uparrow 34}\right)}\right): \pi \left({n}\right) - \displaystyle \int_2^n \frac {\mathrm d x} {\ln x} < 0$

Here, $10 \uparrow \left({10 \uparrow \left({10 \uparrow 34}\right)}\right)$ is Skewes' number.