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Mathbox for Emmett Weisz |
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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 47086 | . 2 class Pg | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | cvv 3443 | . . . 4 class V | |
4 | 2 | cv 1540 | . . . . . 6 class 𝑥 |
5 | 4 | cpw 4558 | . . . . 5 class 𝒫 𝑥 |
6 | 5, 5 | cxp 5629 | . . . 4 class (𝒫 𝑥 × 𝒫 𝑥) |
7 | 2, 3, 6 | cmpt 5186 | . . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)) |
8 | 7 | csetrecs 47060 | . 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
9 | 1, 8 | wceq 1541 | 1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) |
Colors of variables: wff setvar class |
This definition is referenced by: elpg 47091 pgindnf 47093 |
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