Definition df-pg 50521

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 50520	. 2 class Pg
2		vx	. . . 4 setvar 𝑥
3		cvv 3457	. . . 4 class V
4	2	cv 1569	. . . . . 6 class 𝑥
5	4	cpw 4564	. . . . 5 class 𝒫 𝑥
6	5, 5	cxp 5661	. . . 4 class (𝒫 𝑥 × 𝒫 𝑥)
7	2, 3, 6	cmpt 5194	. . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))
8	7	csetrecs 50494	. 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))
9	1, 8	wceq 1570	1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))

This definition is used by:  elpg  50525  pgindnf  50527