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Definition df-un 2978
 Description: Define the union of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with difference (𝐴 ∖ 𝐵) (df-dif 2976) and intersection (𝐴 ∩ 𝐵) (df-in 2980). (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 2972 . 2 class (𝐴𝐵)
4 vx . . . . . 6 setvar 𝑥
54cv 1284 . . . . 5 class 𝑥
65, 1wcel 1434 . . . 4 wff 𝑥𝐴
75, 2wcel 1434 . . . 4 wff 𝑥𝐵
86, 7wo 662 . . 3 wff (𝑥𝐴𝑥𝐵)
98, 4cab 2068 . 2 class {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
103, 9wceq 1285 1 wff (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
 Colors of variables: wff set class This definition is referenced by:  elun  3114  nfun  3129  unipr  3623  iinuniss  3766  bdcun  10811
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