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Definition df-pg 44740
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.)
Assertion
Ref Expression
df-pg Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))

Detailed syntax breakdown of Definition df-pg
StepHypRef Expression
1 cpg 44739 . 2 class Pg
2 vx . . . 4 setvar 𝑥
3 cvv 3492 . . . 4 class V
42cv 1527 . . . . . 6 class 𝑥
54cpw 4535 . . . . 5 class 𝒫 𝑥
65, 5cxp 5546 . . . 4 class (𝒫 𝑥 × 𝒫 𝑥)
72, 3, 6cmpt 5137 . . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))
87csetrecs 44714 . 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))
91, 8wceq 1528 1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  elpg  44744
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