Definition df-bday 27610

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 27607	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27605	. . 3 class No
4	2	cv 1540	. . . 4 class 𝑥
5	4	cdm 5622	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5177	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1541	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27614  bdayfo  27643