Definition df-nelbr 48435

Description: Define negated membership as binary relation. Analogous to df-eprel 5550 (the membership relation). (Contributed by AV, 26-Dec-2021.)

Assertion

Ref	Expression
df-nelbr	⊢ _∉ = {⟨𝑥, 𝑦⟩ ∣ ¬ 𝑥 ∈ 𝑦}

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-nelbr

Step	Hyp	Ref	Expression
1		cnelbr 48434	. 2 class _∉
2		vx	. . . . 5 setvar 𝑥
3		vy	. . . . 5 setvar 𝑦
4	2, 3	wel 2145	. . . 4 wff 𝑥 ∈ 𝑦
5	4	wn 3	. . 3 wff ¬ 𝑥 ∈ 𝑦
6	5, 2, 3	copab 5166	. 2 class {⟨𝑥, 𝑦⟩ ∣ ¬ 𝑥 ∈ 𝑦}
7	1, 6	wceq 1569	1 wff _∉ = {⟨𝑥, 𝑦⟩ ∣ ¬ 𝑥 ∈ 𝑦}

This definition is used by:  dfnelbr2  48436  nelbr  48437  nelbrim  48438