Theorem trggrp

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

	Ref	Expression
Assertion	trggrp	⊢ ( 𝑅 ∈ TopRing → 𝑅 ∈ Grp )

Proof

Step	Hyp	Ref	Expression
1		trgring	⊢ ( 𝑅 ∈ TopRing → 𝑅 ∈ Ring )
2		ringgrp	⊢ ( 𝑅 ∈ Ring → 𝑅 ∈ Grp )
3	1 2	syl	⊢ ( 𝑅 ∈ TopRing → 𝑅 ∈ Grp )