Theorem drnggrp

Description: A division ring is a group. (Contributed by NM, 8-Sep-2011)

	Ref	Expression
Assertion	drnggrp	⊢ ( 𝑅 ∈ DivRing → 𝑅 ∈ Grp )

Proof

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