About the non-trivial zeros of the Riemann zeta function.

Question

We define the function $N(T)$ is the number of non-trivial zeros $ρ$　of the Riemann zeta function which $0<\Im (ρ) <T$ . Then $$ N(T+1)-N(T)=O(\log(T)) \quad (T\to \infty) $$ I understood this property.

But I couldn't understand following claim.

For arbitrarily large T>O and all non-trivial zeros $ρ=β+iγ$ ,We get $$\frac{1}{\log (T)}=O(|T-γ|)$$

This property is used for the proof of the explicit fomula.

Please tell me about this.