Definition df-uni

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 } ( ex-uni ). This is similar to the union of two classes df-un . (Contributed by NM, 23-Aug-1993)

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

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	|- A
1	0	cuni	|- U. A
2		vx	|- x
3		vy	|- y
4	2	cv	|- x
5	3	cv	|- y
6	4 5	wcel	|- x e. y
7	5 0	wcel	|- y e. A
8	6 7	wa	|- ( x e. y /\ y e. A )
9	8 3	wex	|- E. y ( x e. y /\ y e. A )
10	9 2	cab	|- { x | E. y ( x e. y /\ y e. A ) }
11	1 10	wceq	|- U. A = { x | E. y ( x e. y /\ y e. A ) }