Definition df-pg 47745

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 47744	. 2 class Pg
2		vx	. . . 4 setvar 𝑥
3		cvv 3474	. . . 4 class V
4	2	cv 1540	. . . . . 6 class 𝑥
5	4	cpw 4602	. . . . 5 class 𝒫 𝑥
6	5, 5	cxp 5674	. . . 4 class (𝒫 𝑥 × 𝒫 𝑥)
7	2, 3, 6	cmpt 5231	. . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))
8	7	csetrecs 47718	. 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  47749  pgindnf  47751