Is $1+T$ a topological generator for $Z_p[[T]]$ ? Please give a proof/proof idea. ($Z_{p}$ is the ring of p-adic integers)

Consider the ring of formal power series $\mathbb{Z}_p[[T]]$ (where $\mathbb{Z}_p$ denotes the ring of $p$-adic integers) with the topology in which a neighborhood basis for $0$ is given by the ideals $I_{n,m} = \left<p^n,T^m\right>$. Is $1+T$ a topological generator for $\mathbb{Z}_p[[T]]$ (i.e., is $\mathbb{Z}_p[[T]]$ the minimal closed subring containing $1+T$)?