Description: A T_0 space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010)
Ref | Expression | ||
---|---|---|---|
Assertion | t0top | ⊢ ( 𝐽 ∈ Kol2 → 𝐽 ∈ Top ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | ⊢ ∪ 𝐽 = ∪ 𝐽 | |
2 | 1 | ist0 | ⊢ ( 𝐽 ∈ Kol2 ↔ ( 𝐽 ∈ Top ∧ ∀ 𝑥 ∈ ∪ 𝐽 ∀ 𝑦 ∈ ∪ 𝐽 ( ∀ 𝑜 ∈ 𝐽 ( 𝑥 ∈ 𝑜 ↔ 𝑦 ∈ 𝑜 ) → 𝑥 = 𝑦 ) ) ) |
3 | 2 | simplbi | ⊢ ( 𝐽 ∈ Kol2 → 𝐽 ∈ Top ) |