Description: A topological monoid is a topological space. (Contributed by Mario Carneiro, 19-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | tmdtps | |- ( G e. TopMnd -> G e. TopSp ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- ( +f ` G ) = ( +f ` G ) |
|
2 | eqid | |- ( TopOpen ` G ) = ( TopOpen ` G ) |
|
3 | 1 2 | istmd | |- ( G e. TopMnd <-> ( G e. Mnd /\ G e. TopSp /\ ( +f ` G ) e. ( ( ( TopOpen ` G ) tX ( TopOpen ` G ) ) Cn ( TopOpen ` G ) ) ) ) |
4 | 3 | simp2bi | |- ( G e. TopMnd -> G e. TopSp ) |