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	⊢ ℤring ∈ Ring

Proof

Step	Hyp	Ref	Expression
1		zringcrng	⊢ ℤring ∈ CRing
2		crngring	⊢ ( ℤring ∈ CRing → ℤring ∈ Ring )
3	1 2	ax-mp	⊢ ℤring ∈ Ring