Definition df-bday 32762

Description: Finally, we introduce the birthday function. This function maps each surreal to an ordinal. In our implementation, this is the domain of the sign function. The important properties of this function are established later. (Contributed by Scott Fenton, 11-Jun-2011.)

Assertion

Ref	Expression
df-bday	⊢ bday = (𝑥 ∈ No ↦ dom 𝑥)

Detailed syntax breakdown of Definition df-bday

Step	Hyp	Ref	Expression
1		cbday 32759	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 32757	. . 3 class No
4	2	cv 1521	. . . 4 class 𝑥
5	4	cdm 5443	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5041	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1522	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  32765  bdayfo  32792