Definition df-bday 27707

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 27704	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27702	. . 3 class No
4	2	cv 1536	. . . 4 class 𝑥
5	4	cdm 5700	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5249	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1537	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27711  bdayfo  27740