Theorem zringnrg

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

	Ref	Expression
Assertion	zringnrg	⊢ ℤring ∈ NrmRing

Proof

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