Definition df-uni 3784

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 3115. (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 3783	. 2 class U. A
3		vx	. . . . . 6 setvar x
4		vy	. . . . . 6 setvar y
5	3, 4	wel 2136	. . . . 5 wff x e. y
6	4	cv 1341	. . . . . 6 class y
7	6, 1	wcel 2135	. . . . 5 wff y e. A
8	5, 7	wa 103	. . . 4 wff ( x e. y /\ y e. A )
9	8, 4	wex 1479	. . 3 wff E. y ( x e. y /\ y e. A )
10	9, 3	cab 2150	. 2 class { x | E. y ( x e. y /\ y e. A ) }
11	2, 10	wceq 1342	1 wff U. A = { x | E. y ( x e. y /\ y e. A ) }

This definition is referenced by:  dfuni2  3785  eluni  3786  csbunig  3791  unipr  3797  uniuni  4423  bdcuni  13593