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	$$⊢A\cup B=\left\{x|\left(x\in A\vee x\in B\right)\right\}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	$$classA$$
1		cB	$$classB$$
2	0 1	cun	$$class\left(A\cup B\right)$$
3		vx	$$setvarx$$
4	3	cv	$$setvarx$$
5	4 0	wcel	$$wffx\in A$$
6	4 1	wcel	$$wffx\in B$$
7	5 6	wo	$$wff\left(x\in A\vee x\in B\right)$$
8	7 3	cab	$$class\left\{x|\left(x\in A\vee x\in B\right)\right\}$$
9	2 8	wceq	$$wffA\cup B=\left\{x|\left(x\in A\vee x\in B\right)\right\}$$