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	$$⊢\bigcup A=\left\{x|\exists y\left(x\in y\wedge y\in A\right)\right\}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	$$classA$$
1	0	cuni	$$class\bigcup A$$
2		vx	$$setvarx$$
3		vy	$$setvary$$
4	2	cv	$$setvarx$$
5	3	cv	$$setvary$$
6	4 5	wcel	$$wffx\in y$$
7	5 0	wcel	$$wffy\in A$$
8	6 7	wa	$$wff\left(x\in y\wedge y\in A\right)$$
9	8 3	wex	$$wff\exists y\left(x\in y\wedge y\in A\right)$$
10	9 2	cab	$$class\left\{x|\exists y\left(x\in y\wedge y\in A\right)\right\}$$
11	1 10	wceq	$$wff\bigcup A=\left\{x|\exists y\left(x\in y\wedge y\in A\right)\right\}$$