Definition df-bday 27644

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 27641	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27639	. . 3 class No
4	2	cv 1538	. . . 4 class 𝑥
5	4	cdm 5667	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5207	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1539	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27648  bdayfo  27677