Rao–Blackwell theorem

Let $V=V(x_1,x_2,\dots,x_n)$ be an unbiased estimator of $\gamma(\theta)$ and $T$ be a sufficient statistic for $\gamma(\theta)$. Define $\Phi(t)=\mathbb{E}[V\mid T=t]$. Which of the following statements is/are correct?

I. $\Phi(t)$ is an unbiased estimator of $\gamma(\theta)$.

II. The variance of $\Phi(t)$ is less than or equal to variance of $V$.

III. $\Phi(t)$ is a function of sufficient statistic which is dependent on $\theta$.