Definition df-nelbr 41289

Description: Define negated membership as binary relation. Analogous to df-eprel 5029 (the epsilon relation). (Contributed by AV, 26-Dec-2021.)

Assertion

Ref	Expression
df-nelbr	|- _ e// = { <. x , y >. | -. x e. y }

Distinct variable group:   x, y

Detailed syntax breakdown of Definition df-nelbr

Step	Hyp	Ref	Expression
1		cnelbr 41288	. 2 class _ e//
2		vx	. . . . 5 setvar x
3		vy	. . . . 5 setvar y
4	2, 3	wel 1991	. . . 4 wff x e. y
5	4	wn 3	. . 3 wff -. x e. y
6	5, 2, 3	copab 4712	. 2 class { <. x , y >. | -. x e. y }
7	1, 6	wceq 1483	1 wff _ e// = { <. x , y >. | -. x e. y }

This definition is referenced by:  dfnelbr2  41290  nelbr  41291  nelbrim  41292