Definition df-bday 27616

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 27613	. 2 class bday
2		vx	. . 3 setvar 𝑥
3		csur 27611	. . 3 class No
4	2	cv 1541	. . . 4 class 𝑥
5	4	cdm 5625	. . 3 class dom 𝑥
6	2, 3, 5	cmpt 5180	. 2 class (𝑥 ∈ No ↦ dom 𝑥)
7	1, 6	wceq 1542	1 wff bday = (𝑥 ∈ No ↦ dom 𝑥)

This definition is referenced by:  bdayval  27620  bdayfo  27649