Definition df-bday 31798

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 31795	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 31793	. . 3 class No
4	2	cv 1482	. . . 4 class 𝑥
5	4	cdm 5114	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 4729	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1483	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  31801  bdayfo  31828