Definition df-bday 27629

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 27626	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27624	. . 3 class No
4	2	cv 1541	. . . 4 class 𝑥
5	4	cdm 5634	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5181	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1542	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27633  bdayfo  27662