Definition df-bday 27137

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 27134	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27132	. . 3 class No
4	2	cv 1540	. . . 4 class 𝑥
5	4	cdm 5675	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5230	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1541	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27140  bdayfo  27169