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Definition df-goel 32701
Description: Define the Godel-set of membership. Here the arguments 𝑥 = ⟨𝑁, 𝑃 correspond to vN and vP , so (∅∈𝑔1o) 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
StepHypRef Expression
1 cgoe 32694 . 2 class 𝑔
2 vx . . 3 setvar 𝑥
3 com 7564 . . . 4 class ω
43, 3cxp 5521 . . 3 class (ω × ω)
5 c0 4246 . . . 4 class
62cv 1537 . . . 4 class 𝑥
75, 6cop 4534 . . 3 class ⟨∅, 𝑥
82, 4, 7cmpt 5113 . 2 class (𝑥 ∈ (ω × ω) ↦ ⟨∅, 𝑥⟩)
91, 8wceq 1538 1 wff 𝑔 = (𝑥 ∈ (ω × ω) ↦ ⟨∅, 𝑥⟩)
Colors of variables: wff setvar class
This definition is referenced by:  goel  32708
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