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Definition df-nelbr 43348
Description: Define negated membership as binary relation. Analogous to df-eprel 5458 (the membership relation). (Contributed by AV, 26-Dec-2021.)
Assertion
Ref Expression
df-nelbr _∉ = {⟨𝑥, 𝑦⟩ ∣ ¬ 𝑥𝑦}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-nelbr
StepHypRef Expression
1 cnelbr 43347 . 2 class _∉
2 vx . . . . 5 setvar 𝑥
3 vy . . . . 5 setvar 𝑦
42, 3wel 2106 . . . 4 wff 𝑥𝑦
54wn 3 . . 3 wff ¬ 𝑥𝑦
65, 2, 3copab 5119 . 2 class {⟨𝑥, 𝑦⟩ ∣ ¬ 𝑥𝑦}
71, 6wceq 1528 1 wff _∉ = {⟨𝑥, 𝑦⟩ ∣ ¬ 𝑥𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  dfnelbr2  43349  nelbr  43350  nelbrim  43351
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