Theorem zringcrng

Description: The ring of integers is a commutative ring. (Contributed by AV, 13-Jun-2019)

	Ref	Expression
Assertion	zringcrng	⊢ ℤring ∈ CRing

Proof

Step	Hyp	Ref	Expression
1		cncrng	⊢ ℂfld ∈ CRing
2		zsubrg	⊢ ℤ ∈ ( SubRing ‘ ℂfld )
3		df-zring	⊢ ℤring = ( ℂfld ↾s ℤ )
4	3	subrgcrng	⊢ ( ( ℂfld ∈ CRing ∧ ℤ ∈ ( SubRing ‘ ℂfld ) ) → ℤring ∈ CRing )
5	1 2 4	mp2an	⊢ ℤring ∈ CRing