Description: A topological group is a group. (Contributed by FL, 18-Apr-2010) (Revised by Mario Carneiro, 13-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | tgpgrp | |- ( G e. TopGrp -> G e. Grp ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- ( TopOpen ` G ) = ( TopOpen ` G ) |
|
2 | eqid | |- ( invg ` G ) = ( invg ` G ) |
|
3 | 1 2 | istgp | |- ( G e. TopGrp <-> ( G e. Grp /\ G e. TopMnd /\ ( invg ` G ) e. ( ( TopOpen ` G ) Cn ( TopOpen ` G ) ) ) ) |
4 | 3 | simp1bi | |- ( G e. TopGrp -> G e. Grp ) |