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Metamath Proof Explorer

Theorem idomringd

Description: An integral domain is a ring. (Contributed by Thierry Arnoux, 22-Mar-2025)

		Ref	Expression
	Hypothesis	idomringd.1	$⊢ φ \to R \in IDomn$
	Assertion	idomringd	$⊢ φ \to R \in Ring$

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