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Metamath Proof Explorer

Theorem t1top

Description: A T_1 space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010)

Ref Expression
Assertion t1top ⊢ J ∈ Fre → J ∈ Top

Proof

Step Hyp Ref Expression
1 eqid ⊢ ⋃ J = ⋃ J
2 1 ist1 ⊢ J ∈ Fre ↔ J ∈ Top ∧ ∀ x ∈ ⋃ J x ∈ Clsd ⁡ J
3 2 simplbi ⊢ J ∈ Fre → J ∈ Top