Metamath Proof Explorer


Theorem tdrgring

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

Ref Expression
Assertion tdrgring ( 𝑅 ∈ TopDRing → 𝑅 ∈ Ring )

Proof

Step Hyp Ref Expression
1 tdrgtrg ( 𝑅 ∈ TopDRing → 𝑅 ∈ TopRing )
2 trgring ( 𝑅 ∈ TopRing → 𝑅 ∈ Ring )
3 1 2 syl ( 𝑅 ∈ TopDRing → 𝑅 ∈ Ring )