Definition df-uni 2499

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 2498	. 2 class U.A
3		vx	. . . . . . 7 set x
4	3	cv 953	. . . . . 6 class x
5		vy	. . . . . . 7 set y
6	5	cv 953	. . . . . 6 class y
7	4, 6	wcel 956	. . . . 5 wff x e. y
8	6, 1	wcel 956	. . . . 5 wff y e. A
9	7, 8	wa 223	. . . 4 wff (x e. y /\ y e. A)
10	9, 5	wex 978	. . 3 wff E.y(x e. y /\ y e. A)
11	10, 3	cab 1461	. 2 class {x | E.y(x e. y /\ y e. A)}
12	2, 11	wceq 954	1 wff U.A = {x | E.y(x e. y /\ y e. A)}

This definition is referenced by:  dfuni2 2500  eluni 2501  unieq 2505  unipr 2510  uniss 2516  dfiun2g 2581  uniuni 2875

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