Description: A topological monoid is a topological space. (Contributed by Mario Carneiro, 19-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | tmdtps | ⊢ ( 𝐺 ∈ TopMnd → 𝐺 ∈ TopSp ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | ⊢ ( +𝑓 ‘ 𝐺 ) = ( +𝑓 ‘ 𝐺 ) | |
2 | eqid | ⊢ ( TopOpen ‘ 𝐺 ) = ( TopOpen ‘ 𝐺 ) | |
3 | 1 2 | istmd | ⊢ ( 𝐺 ∈ TopMnd ↔ ( 𝐺 ∈ Mnd ∧ 𝐺 ∈ TopSp ∧ ( +𝑓 ‘ 𝐺 ) ∈ ( ( ( TopOpen ‘ 𝐺 ) ×t ( TopOpen ‘ 𝐺 ) ) Cn ( TopOpen ‘ 𝐺 ) ) ) ) |
4 | 3 | simp2bi | ⊢ ( 𝐺 ∈ TopMnd → 𝐺 ∈ TopSp ) |