Definition df-un 3579

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 27281). Contrast this operation with difference ( A \ B ) (df-dif 3577) and intersection ( A i^i B ) (df-in 3581). For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 3859. For union defined in terms of intersection, see dfun3 3865. (Contributed by NM, 23-Aug-1993.)

Assertion

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

Distinct variable groups:   x, A   x, B

Detailed syntax breakdown of Definition df-un

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	cun 3572	. 2 class ( A u. B )
4		vx	. . . . . 6 setvar x
5	4	cv 1482	. . . . 5 class x
6	5, 1	wcel 1990	. . . 4 wff x e. A
7	5, 2	wcel 1990	. . . 4 wff x e. B
8	6, 7	wo 383	. . 3 wff ( x e. A \/ x e. B )
9	8, 4	cab 2608	. 2 class { x | ( x e. A \/ x e. B ) }
10	3, 9	wceq 1483	1 wff ( A u. B ) = { x | ( x e. A \/ x e. B ) }

This definition is referenced by:  elun  3753  nfun  3769  unipr  4449  iinuni  4609  fvclss  6500  bnj98  30937