Theorem trggrp

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

	Ref	Expression
Assertion	trggrp	$$⊢R\in \mathrm{TopRing}\to R\in \mathrm{Grp}$$

Proof

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