RH & explicit formula for the number of primes $ \le x$

Question

Does the RH have to be true in order for Riemann's explicit formula for the number of primes <= x to hold? The formula is (copied from wikipedia:https://en.wikipedia.org/wiki/Explicit_formulae_(L-function)): $f(x) = li(x)-\sum_{\rho}li(x^{\rho})-\log 2 +\int_x^\infty\frac{dt}{t(t^2-1)log t}$ where $f(x) = \pi_0(x)+(1/2)\pi_0(x^{1/2})+ \ldots$ where $\pi_0$ is the normalised prime counting function. In other words, does this formula hold even if not all the critical roots are on the critical line x = 1/2?