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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-pg | Structured version Visualization version GIF version |
Description: Define the class of partizan games. More precisely, this is the class of partizan game forms, many of which represent equal partisan games. In metamath, equality between partizan games is represented by a different equivalence relation than class equality. (Contributed by Emmett Weisz, 22-Aug-2021.) |
Ref | Expression |
---|---|
df-pg | ⊢ Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpg 42452 | . 2 class Pg | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | cvv 3200 | . . . 4 class V | |
4 | 2 | cv 1482 | . . . . . 6 class 𝑥 |
5 | 4 | cpw 4158 | . . . . 5 class 𝒫 𝑥 |
6 | 5, 5 | cxp 5112 | . . . 4 class (𝒫 𝑥 × 𝒫 𝑥) |
7 | 2, 3, 6 | cmpt 4729 | . . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)) |
8 | 7 | csetrecs 42430 | . 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
9 | 1, 8 | wceq 1483 | 1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
Colors of variables: wff setvar class |
This definition is referenced by: elpg 42457 |
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