Locally connected and no proper open subgroup implies connected

Statement
Suppose $$G$$ is a topological group that is locally connected and has no proper open subgroup. Then, $$G$$ is a proves property satisfaction of::connected topological group.

Facts used

 * 1) uses::Locally connected implies connected component of identity is open subgroup

Related facts

 * Connected implies no proper open subgroup
 * No proper open subgroup not implies connected

Proof
The proof follows directly from Fact (1).