Definition df-bday 27889

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 27886	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27884	. . 3 class No
4	2	cv 1569	. . . 4 class 𝑥
5	4	cdm 5659	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5190	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1570	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is used by:  bdayval  27892  bdayfo  27921