Definition df-bday 27627

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 27624	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27622	. . 3 class No
4	2	cv 1546	. . . 4 class 𝑥
5	4	cdm 5619	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5154	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1547	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27631  bdayfo  27660