Definition df-un

Description: Define the union of two classes. Definition 5.6 of TakeutiZaring p. 16. For example, ( { 1 , 3 } u. { 1 , 8 } ) = { 1 , 3 , 8 } ( ex-un ). Contrast this operation with difference ( A \ B ) ( df-dif ) and intersection ( A i^i B ) ( df-in ). For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 . For union defined in terms of intersection, see dfun3 . (Contributed by NM, 23-Aug-1993)

	Ref	Expression
Assertion	df-un	|- ( A u. B ) = { x | ( x e. A \/ x e. B ) }

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	|- A
1		cB	|- B
2	0 1	cun	|- ( A u. B )
3		vx	|- x
4	3	cv	|- x
5	4 0	wcel	|- x e. A
6	4 1	wcel	|- x e. B
7	5 6	wo	|- ( x e. A \/ x e. B )
8	7 3	cab	|- { x | ( x e. A \/ x e. B ) }
9	2 8	wceq	|- ( A u. B ) = { x | ( x e. A \/ x e. B ) }