Definition df-pg 46659

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 46658	. 2 class Pg
2		vx	. . . 4 setvar 𝑥
3		cvv 3437	. . . 4 class V
4	2	cv 1538	. . . . . 6 class 𝑥
5	4	cpw 4539	. . . . 5 class 𝒫 𝑥
6	5, 5	cxp 5598	. . . 4 class (𝒫 𝑥 × 𝒫 𝑥)
7	2, 3, 6	cmpt 5164	. . 3 class (𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥))
8	7	csetrecs 46633	. 2 class setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))
9	1, 8	wceq 1539	1 wff Pg = setrecs((𝑥 ∈ V ↦ (𝒫 𝑥 × 𝒫 𝑥)))

This definition is referenced by:  elpg  46663