df-zs - Metamath Proof Explorer

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Definition df-zs 28758

Description: Define the surreal integers. Compare dfz2 12705. (Contributed by Scott Fenton, 17-May-2025.)

**Assertion**
Ref	Expression
df-zs	⊢ ℤ_s = ( -_s “ (ℕ_s × ℕ_s))

**Detailed syntax breakdown of Definition df-zs**
Step	Hyp	Ref	Expression
1		czs 28757	. 2 class ℤ_s
2		csubs 28399	. . 3 class -_s
3		cnns 28692	. . . 4 class ℕ_s
4	3, 3	cxp 5649	. . 3 class (ℕ_s × ℕ_s)
5	2, 4	cima 5654	. 2 class ( -_s “ (ℕ_s × ℕ_s))
6	1, 5	wceq 1570	1 wff ℤ_s = ( -_s “ (ℕ_s × ℕ_s))

Colors of variables: wff setvar class

This definition is used by: zsex 28759 zssno 28760 elzs 28763