Definition df-bday 27556

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 27553	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27551	. . 3 class No
4	2	cv 1539	. . . 4 class 𝑥
5	4	cdm 5638	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5188	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1540	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27560  bdayfo  27589