Theorem zringbas

Description: The integers are the base of the ring of integers. (Contributed by Thierry Arnoux, 31-Oct-2017) (Revised by AV, 9-Jun-2019)

	Ref	Expression
Assertion	zringbas	⊢ ℤ = ( Base ‘ ℤring )

Proof

Step	Hyp	Ref	Expression
1		zsscn	⊢ ℤ ⊆ ℂ
2		df-zring	⊢ ℤring = ( ℂfld ↾s ℤ )
3		cnfldbas	⊢ ℂ = ( Base ‘ ℂfld )
4	2 3	ressbas2	⊢ ( ℤ ⊆ ℂ → ℤ = ( Base ‘ ℤring ) )
5	1 4	ax-mp	⊢ ℤ = ( Base ‘ ℤring )