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Definition df-uni 4631
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} (ex-uni 27610). This is similar to the union of two classes df-un 3774. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
df-uni 𝐴 = {𝑥 ∣ ∃𝑦(𝑥𝑦𝑦𝐴)}
Distinct variable group:   𝑥,𝑦,𝐴

Detailed syntax breakdown of Definition df-uni
StepHypRef Expression
1 cA . . 3 class 𝐴
21cuni 4630 . 2 class 𝐴
3 vx . . . . . 6 setvar 𝑥
4 vy . . . . . 6 setvar 𝑦
53, 4wel 2157 . . . . 5 wff 𝑥𝑦
64cv 1636 . . . . . 6 class 𝑦
76, 1wcel 2156 . . . . 5 wff 𝑦𝐴
85, 7wa 384 . . . 4 wff (𝑥𝑦𝑦𝐴)
98, 4wex 1859 . . 3 wff 𝑦(𝑥𝑦𝑦𝐴)
109, 3cab 2792 . 2 class {𝑥 ∣ ∃𝑦(𝑥𝑦𝑦𝐴)}
112, 10wceq 1637 1 wff 𝐴 = {𝑥 ∣ ∃𝑦(𝑥𝑦𝑦𝐴)}
Colors of variables: wff setvar class
This definition is referenced by:  dfuni2  4632  eluni  4633  unipr  4643  csbuni  4660  uniuni  7197  csbunigVD  39622
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