Theorem tdrgring

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

	Ref	Expression
Assertion	tdrgring	$$⊢R\in \mathrm{TopDRing}\to R\in \mathrm{Ring}$$

Proof

Step	Hyp	Ref	Expression
1		tdrgtrg	$$⊢R\in \mathrm{TopDRing}\to R\in \mathrm{TopRing}$$
2		trgring	$$⊢R\in \mathrm{TopRing}\to R\in \mathrm{Ring}$$
3	1 2	syl	$$⊢R\in \mathrm{TopDRing}\to R\in \mathrm{Ring}$$