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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-pg | Structured version Visualization version GIF version |
Description: Define the class of partisan games. More precisely, this is the class of partisan game forms, many of which represent equal partisan games. In Metamath, equality between partisan 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 46085 | . 2 class Pg | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | cvv 3408 | . . . 4 class V | |
4 | 2 | cv 1542 | . . . . . 6 class 𝑥 |
5 | 4 | cpw 4513 | . . . . 5 class 𝒫 𝑥 |
6 | 5, 5 | cxp 5549 | . . . 4 class (𝒫 𝑥 × 𝒫 𝑥) |
7 | 2, 3, 6 | cmpt 5135 | . . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)) |
8 | 7 | csetrecs 46060 | . 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
9 | 1, 8 | wceq 1543 | 1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
Colors of variables: wff setvar class |
This definition is referenced by: elpg 46090 |
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