Ordinate of zeros of zeta Riemann function

Question

In the book: Multiplicative Number Theory, Davenport, we see that there is a bound for ordinates of zeros of zeta Riemann function ($s=\beta+i\gamma$ is zero of zeta function)

My question is that how can we prove that $\gamma_1$ (the smallest positive $\gamma$ among zeros of zeta function) is bigger or equal to 6.5, i.e. $\gamma_1>=6.5$?

Thanks for your help!