Metamath Proof Explorer


Definition df-bday

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)

Ref Expression
Assertion df-bday bday = ( 𝑥 No ↦ dom 𝑥 )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cbday bday
1 vx 𝑥
2 csur No
3 1 cv 𝑥
4 3 cdm dom 𝑥
5 1 2 4 cmpt ( 𝑥 No ↦ dom 𝑥 )
6 0 5 wceq bday = ( 𝑥 No ↦ dom 𝑥 )