|   | Mathbox for Emmett Weisz | < Previous  
      Next > Nearby theorems | |
| 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 49228 | . 2 class Pg | |
| 2 | vx | . . . 4 setvar 𝑥 | |
| 3 | cvv 3480 | . . . 4 class V | |
| 4 | 2 | cv 1539 | . . . . . 6 class 𝑥 | 
| 5 | 4 | cpw 4600 | . . . . 5 class 𝒫 𝑥 | 
| 6 | 5, 5 | cxp 5683 | . . . 4 class (𝒫 𝑥 × 𝒫 𝑥) | 
| 7 | 2, 3, 6 | cmpt 5225 | . . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)) | 
| 8 | 7 | csetrecs 49202 | . 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) | 
| 9 | 1, 8 | wceq 1540 | 1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: elpg 49233 pgindnf 49235 | 
| Copyright terms: Public domain | W3C validator |