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Metamath Proof Explorer

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 ) }