Theorem idomringd

Description: An integral domain is a ring. (Contributed by Jeff Madsen, 6-Jan-2011) (Revised by Thierry Arnoux, 22-Mar-2025)

	Ref	Expression
Hypothesis	idomringd.1	$$⊢\phi \to R\in \mathrm{IDomn}$$
Assertion	idomringd	$$⊢\phi \to R\in \mathrm{Ring}$$

Proof

Step	Hyp	Ref	Expression
1		idomringd.1	$$⊢\phi \to R\in \mathrm{IDomn}$$
2	1	idomcringd	$$⊢\phi \to R\in \mathrm{CRing}$$
3	2	crngringd	$$⊢\phi \to R\in \mathrm{Ring}$$