Definition df-bday 33775

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 33772	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 33770	. . 3 class No
4	2	cv 1538	. . . 4 class 𝑥
5	4	cdm 5580	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5153	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1539	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  33778  bdayfo  33807