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Metamath Proof Explorer

Theorem zringring

Description: The ring of integers is a ring. (Contributed by AV, 20-May-2019) (Revised by AV, 9-Jun-2019) (Proof shortened by AV, 13-Jun-2019)

		Ref	Expression
	Assertion	zringring	$⊢ ℤ_{ring} \in Ring$

Step	Hyp	Ref	Expression
1		zringcrng	$⊢ ℤ_{ring} \in CRing$
2		crngring	$⊢ ℤ_{ring} \in CRing \to ℤ_{ring} \in Ring$
3	1 2	ax-mp	$⊢ ℤ_{ring} \in Ring$