Definition df-uni 2494

Description: Define the union of a class i.e. the collection of all members of the members of the class. Definition 5.5 of [TakeutiZaring] p. 16.

Assertion

Ref	Expression
df-uni	|- U.A = {x | E.y(x e. y /\ y e. A)}

Distinct variable group:   x,y,A

Detailed syntax breakdown of Definition df-uni

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	cuni 2493	. 2 class U.A
3		vx	. . . . . . 7 set x
4	3	cv 952	. . . . . 6 class x
5		vy	. . . . . . 7 set y
6	5	cv 952	. . . . . 6 class y
7	4, 6	wcel 955	. . . . 5 wff x e. y
8	6, 1	wcel 955	. . . . 5 wff y e. A
9	7, 8	wa 223	. . . 4 wff (x e. y /\ y e. A)
10	9, 5	wex 977	. . 3 wff E.y(x e. y /\ y e. A)
11	10, 3	cab 1456	. 2 class {x | E.y(x e. y /\ y e. A)}
12	2, 11	wceq 953	1 wff U.A = {x | E.y(x e. y /\ y e. A)}

This definition is referenced by:  dfuni2 2495  eluni 2496  unieq 2500  unipr 2505  uniss 2511  dfiun2g 2576  uniuni 2870

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