Definition df-uni 3840

Description: Define the union of a class i.e. the collection of all members of the members of the class. Definition 5.5 of [TakeutiZaring] p. 16. For example, U. { { 1 , 3 } , { 1 , 8 } } = { 1 , 3 , 8 }. This is similar to the union of two classes df-un 3161. (Contributed by NM, 23-Aug-1993.)

Assertion

Ref	Expression
df-uni	|- U. A = { x | E. y ( x e. y /\ y e. A ) }

Distinct variable group:   x, y, A

Detailed syntax breakdown of Definition df-uni

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	cuni 3839	. 2 class U. A
3		vx	. . . . . 6 setvar x
4		vy	. . . . . 6 setvar y
5	3, 4	wel 2168	. . . . 5 wff x e. y
6	4	cv 1363	. . . . . 6 class y
7	6, 1	wcel 2167	. . . . 5 wff y e. A
8	5, 7	wa 104	. . . 4 wff ( x e. y /\ y e. A )
9	8, 4	wex 1506	. . 3 wff E. y ( x e. y /\ y e. A )
10	9, 3	cab 2182	. 2 class { x | E. y ( x e. y /\ y e. A ) }
11	2, 10	wceq 1364	1 wff U. A = { x | E. y ( x e. y /\ y e. A ) }

This definition is referenced by:  dfuni2  3841  eluni  3842  csbunig  3847  unipr  3853  uniuni  4486  bdcuni  15522