Definition df-bday 27704

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 27701	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27699	. . 3 class No
4	2	cv 1536	. . . 4 class 𝑥
5	4	cdm 5689	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5231	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1537	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27708  bdayfo  27737