Definition df-goel 33281

Description: Define the Godel-set of membership. Here the arguments 𝑥 = ⟨𝑁, 𝑃⟩ correspond to v_N and v_P , so (∅∈_𝑔1_o) actually means v₀ ∈ v₁ , not 0 ∈ 1. (Contributed by Mario Carneiro, 14-Jul-2013.)

Assertion

Ref	Expression
df-goel	⊢ ∈𝑔 = (𝑥 ∈ (ω × ω) ↦ ⟨∅, 𝑥⟩)

Detailed syntax breakdown of Definition df-goel

Step	Hyp	Ref	Expression
1		cgoe 33274	. 2 class ∈𝑔
2		vx	. . 3 setvar 𝑥
3		com 7700	. . . 4 class ω
4	3, 3	cxp 5586	. . 3 class (ω × ω)
5		c0 4261	. . . 4 class ∅
6	2	cv 1540	. . . 4 class 𝑥
7	5, 6	cop 4572	. . 3 class ⟨∅, 𝑥⟩
8	2, 4, 7	cmpt 5161	. 2 class (𝑥 ∈ (ω × ω) ↦ ⟨∅, 𝑥⟩)
9	1, 8	wceq 1541	1 wff ∈𝑔 = (𝑥 ∈ (ω × ω) ↦ ⟨∅, 𝑥⟩)

This definition is referenced by:  goel  33288