Definition df-se 4456

Description: Define the set-like predicate. (Contributed by Mario Carneiro, 19-Nov-2014.)

Assertion

Ref	Expression
df-se	|- ( R Se A <-> A. x e. A { y e. A | y R x } e. _V )

Distinct variable groups:   x, y, R   x, A, y

Detailed syntax breakdown of Definition df-se

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cR	. . 3 class R
3	1, 2	wse 4452	. 2 wff R Se A
4		vy	. . . . . . 7 setvar y
5	4	cv 1397	. . . . . 6 class y
6		vx	. . . . . . 7 setvar x
7	6	cv 1397	. . . . . 6 class x
8	5, 7, 2	wbr 4111	. . . . 5 wff y R x
9	8, 4, 1	crab 2526	. . . 4 class { y e. A | y R x }
10		cvv 2815	. . . 4 class _V
11	9, 10	wcel 2205	. . 3 wff { y e. A | y R x } e. _V
12	11, 6, 1	wral 2522	. 2 wff A. x e. A { y e. A | y R x } e. _V
13	3, 12	wb 105	1 wff ( R Se A <-> A. x e. A { y e. A | y R x } e. _V )

This definition is referenced by:  seex  4458  exse  4459  sess1  4460  sess2  4461  nfse  4464  epse  4465  seinxp  4823  dfse2  5137  exse2  5138