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 )