Definition df-bday 27710

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 27707	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27705	. . 3 class No
4	2	cv 1560	. . . 4 class 𝑥
5	4	cdm 5648	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5182	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1561	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27713  bdayfo  27742