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 )