Definition df-un 3181

Description: Define the union of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with difference ( A \ B ) (df-dif 3179) and intersection ( A i^i B ) (df-in 3183). (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 3175	. 2 class ( A u. B )
4		vx	. . . . . 6 setvar x
5	4	cv 1374	. . . . 5 class x
6	5, 1	wcel 2180	. . . 4 wff x e. A
7	5, 2	wcel 2180	. . . 4 wff x e. B
8	6, 7	wo 712	. . 3 wff ( x e. A \/ x e. B )
9	8, 4	cab 2195	. 2 class { x | ( x e. A \/ x e. B ) }
10	3, 9	wceq 1375	1 wff ( A u. B ) = { x | ( x e. A \/ x e. B ) }

This definition is referenced by:  elun  3325  nfun  3340  unipr  3881  iinuniss  4027  bdcun  16135