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Definition df-un 3565
Description: Define the union of two classes. Definition 5.6 of [TakeutiZaring] p. 16. For example, ({1, 3} ∪ {1, 8}) = {1, 3, 8} (ex-un 27129). Contrast this operation with difference (𝐴𝐵) (df-dif 3563) and intersection (𝐴𝐵) (df-in 3567). For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 3842. For union defined in terms of intersection, see dfun3 3846. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
df-un (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵

Detailed syntax breakdown of Definition df-un
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2cun 3558 . 2 class (𝐴𝐵)
4 vx . . . . . 6 setvar 𝑥
54cv 1479 . . . . 5 class 𝑥
65, 1wcel 1992 . . . 4 wff 𝑥𝐴
75, 2wcel 1992 . . . 4 wff 𝑥𝐵
86, 7wo 383 . . 3 wff (𝑥𝐴𝑥𝐵)
98, 4cab 2612 . 2 class {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
103, 9wceq 1480 1 wff (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Colors of variables: wff setvar class
This definition is referenced by:  elun  3736  nfun  3752  unipr  4420  iinuni  4580  fvclss  6455  bnj98  30637
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