Definition df-bday 28017

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 28014	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 28012	. . 3 class No
4	2	cv 1568	. . . 4 class 𝑥
5	4	cdm 5655	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5189	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1569	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is used by:  bdayval  28020  bdayfo  28049