Definition df-iun 1996

Description: Define indexed union. Ordinarily, A would be independent of x and B would depend on x. In this case x is called an index, A is called an index set, and B is called an indexed set. In most books, x ∈ A is written as a subscript or underneath the ∪. Definition of [Stoll] p. 45.

Assertion

Ref	Expression
df-iun	⊢ ∪x ∈ A B = {y∣∃x ∈ A y ∈ B}

Distinct variable group(s):   x,y   y,A   y,B

Detailed syntax breakdown of Definition df-iun

Step	Hyp	Ref	Expression
1		vx	. . 3 set x
2		cA	. . 3 class A
3		cB	. . 3 class B
4	1, 2, 3	ciun 1994	. 2 class ∪x ∈ A B
5		vy	. . . . . 6 set y
6	5	cv 1089	. . . . 5 class y
7	6, 3	wcel 1092	. . . 4 wff y ∈ B
8	7, 1, 2	wrex 1202	. . 3 wff ∃x ∈ A y ∈ B
9	8, 5	cab 1090	. 2 class {y∣∃x ∈ A y ∈ B}
10	4, 9	wceq 1091	1 wff ∪x ∈ A B = {y∣∃x ∈ A y ∈ B}

This definition is referenced by:  eliun 1998  iunss1 2002  hbiu1 2012  dfiun2 2014  cbviunv 2016  uniiun 2026  abrexex2 2915

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