Metamath Proof Explorer

Theorem lringring

Description: A local ring is a ring. (Contributed by Jim Kingdon, 20-Feb-2025) (Revised by SN, 23-Feb-2025)

		Ref	Expression
	Assertion	lringring	$⊢ R \in LRing \to R \in Ring$

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