Metamath Proof Explorer


Theorem trgtps

Description: A topological ring is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015)

Ref Expression
Assertion trgtps ( 𝑅 ∈ TopRing → 𝑅 ∈ TopSp )

Proof

Step Hyp Ref Expression
1 trgtgp ( 𝑅 ∈ TopRing → 𝑅 ∈ TopGrp )
2 tgptps ( 𝑅 ∈ TopGrp → 𝑅 ∈ TopSp )
3 1 2 syl ( 𝑅 ∈ TopRing → 𝑅 ∈ TopSp )