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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bday | Structured version Visualization version GIF version |
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 |
---|---|
df-bday | ⊢ bday = (𝑥 ∈ No ↦ dom 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbday 33046 | . 2 class bday | |
2 | vx | . . 3 setvar 𝑥 | |
3 | csur 33044 | . . 3 class No | |
4 | 2 | cv 1527 | . . . 4 class 𝑥 |
5 | 4 | cdm 5548 | . . 3 class dom 𝑥 |
6 | 2, 3, 5 | cmpt 5137 | . 2 class (𝑥 ∈ No ↦ dom 𝑥) |
7 | 1, 6 | wceq 1528 | 1 wff bday = (𝑥 ∈ No ↦ dom 𝑥) |
Colors of variables: wff setvar class |
This definition is referenced by: bdayval 33052 bdayfo 33079 |
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