Metamath Proof Explorer


Definition df-uni

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. For example, U. { { 1 , 3 } , { 1 , 8 } } = { 1 , 3 , 8 } ( ex-uni ). This is similar to the union of two classes df-un . (Contributed by NM, 23-Aug-1993)

Ref Expression
Assertion df-uni A = x | y x y y A

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA class A
1 0 cuni class A
2 vx setvar x
3 vy setvar y
4 2 cv setvar x
5 3 cv setvar y
6 4 5 wcel wff x y
7 5 0 wcel wff y A
8 6 7 wa wff x y y A
9 8 3 wex wff y x y y A
10 9 2 cab class x | y x y y A
11 1 10 wceq wff A = x | y x y y A