Definition df-pg 49742

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 49741	. 2 class Pg
2		vx	. . . 4 setvar 𝑥
3		cvv 3436	. . . 4 class V
4	2	cv 1540	. . . . . 6 class 𝑥
5	4	cpw 4545	. . . . 5 class 𝒫 𝑥
6	5, 5	cxp 5609	. . . 4 class (𝒫 𝑥 × 𝒫 𝑥)
7	2, 3, 6	cmpt 5167	. . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))
8	7	csetrecs 49715	. 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))
9	1, 8	wceq 1541	1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))

This definition is referenced by:  elpg  49746  pgindnf  49748