Equivalent definition of profinite group

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Sorry for my bad English.

Let $G$ be a topological group, then we say $G$ is profinite if $G$ satisfies next equivalent condition as follow;

(i) $G$ is compact, Hausdorff, totally disconnected.

(ii)$G$ is compact, Hausdorff, unit element $1\in G$ has neighbourhood system consisted of normal subgroup.

But I can't understand why there are equivalent. Please tell me this proof or reference or hint, thanks.