Theorem dmnrngo

Description: A domain is a ring. (Contributed by Jeff Madsen, 6-Jan-2011)

	Ref	Expression
Assertion	dmnrngo	$$⊢R\in \mathrm{Dmn}\to R\in \mathrm{RingOps}$$

Proof

Step	Hyp	Ref	Expression
1		dmncrng	$$⊢R\in \mathrm{Dmn}\to R\in \mathrm{CRingOps}$$
2		crngorngo	$$⊢R\in \mathrm{CRingOps}\to R\in \mathrm{RingOps}$$
3	1 2	syl	$$⊢R\in \mathrm{Dmn}\to R\in \mathrm{RingOps}$$