Definition df-bday 33534

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 33531	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 33529	. . 3 class No
4	2	cv 1542	. . . 4 class 𝑥
5	4	cdm 5536	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5120	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1543	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  33537  bdayfo  33566