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Definition df-uni 4581
 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 27586). This is similar to the union of two classes df-un 3712. (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 4580 . 2 class 𝐴
3 vx . . . . . 6 setvar 𝑥
4 vy . . . . . 6 setvar 𝑦
53, 4wel 2132 . . . . 5 wff 𝑥𝑦
64cv 1623 . . . . . 6 class 𝑦
76, 1wcel 2131 . . . . 5 wff 𝑦𝐴
85, 7wa 383 . . . 4 wff (𝑥𝑦𝑦𝐴)
98, 4wex 1845 . . 3 wff 𝑦(𝑥𝑦𝑦𝐴)
109, 3cab 2738 . 2 class {𝑥 ∣ ∃𝑦(𝑥𝑦𝑦𝐴)}
112, 10wceq 1624 1 wff 𝐴 = {𝑥 ∣ ∃𝑦(𝑥𝑦𝑦𝐴)}
 Colors of variables: wff setvar class This definition is referenced by:  dfuni2  4582  eluni  4583  unipr  4593  csbuni  4610  uniuni  7128  csbunigVD  39625
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