Definition df-bday 27775

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 27772	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27770	. . 3 class No
4	2	cv 1566	. . . 4 class 𝑥
5	4	cdm 5662	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5196	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1567	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27778  bdayfo  27807