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Metamath Proof Explorer

Theorem domnring

Description: A domain is a ring. (Contributed by Mario Carneiro, 28-Mar-2015)

		Ref	Expression
	Assertion	domnring	$⊢ R \in Domn \to R \in Ring$

Step	Hyp	Ref	Expression
1		domnnzr	$⊢ R \in Domn \to R \in NzRing$
2		nzrring	$⊢ R \in NzRing \to R \in Ring$
3	1 2	syl	$⊢ R \in Domn \to R \in Ring$