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Definition df-uni 3572
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, { { 1 , 3 } , { 1 , 8 } } = { 1 , 3 , 8 } . This is similar to the union of two classes df-un 2916. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
df-uni A = {xy(x y y A)}
Distinct variable group:   x,y,A

Detailed syntax breakdown of Definition df-uni
StepHypRef Expression
1 cA . . 3 class A
21cuni 3571 . 2 class A
3 vx . . . . . 6 setvar x
4 vy . . . . . 6 setvar y
53, 4wel 1391 . . . . 5 wff x y
64cv 1241 . . . . . 6 class y
76, 1wcel 1390 . . . . 5 wff y A
85, 7wa 97 . . . 4 wff (x y y A)
98, 4wex 1378 . . 3 wff y(x y y A)
109, 3cab 2023 . 2 class {xy(x y y A)}
112, 10wceq 1242 1 wff A = {xy(x y y A)}
Colors of variables: wff set class
This definition is referenced by:  dfuni2  3573  eluni  3574  csbunig  3579  unipr  3585  uniuni  4149  bdcuni  9311
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