Definition df-pg 50292

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

Step	Hyp	Ref	Expression
1		cpg 50291	. 2 class Pg
2		vx	. . . 4 setvar 𝑥
3		cvv 3453	. . . 4 class V
4	2	cv 1558	. . . . . 6 class 𝑥
5	4	cpw 4552	. . . . 5 class 𝒫 𝑥
6	5, 5	cxp 5641	. . . 4 class (𝒫 𝑥 × 𝒫 𝑥)
7	2, 3, 6	cmpt 5178	. . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))
8	7	csetrecs 50265	. 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))
9	1, 8	wceq 1559	1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))

This definition is referenced by:  elpg  50296  pgindnf  50298