Definition df-un 3892

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 28774). Contrast this operation with difference (𝐴 ∖ 𝐵) (df-dif 3890) and intersection (𝐴 ∩ 𝐵) (df-in 3894). For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 4194. For union defined in terms of intersection, see dfun3 4200. (Contributed by NM, 23-Aug-1993.)

Assertion

Ref	Expression
df-un	⊢ (𝐴 ∪ 𝐵) = {𝑥 ∣ (𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵)}

Distinct variable groups:   𝑥,𝐴   𝑥,𝐵

Detailed syntax breakdown of Definition df-un

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3	1, 2	cun 3885	. 2 class (𝐴 ∪ 𝐵)
4		vx	. . . . . 6 setvar 𝑥
5	4	cv 1538	. . . . 5 class 𝑥
6	5, 1	wcel 2106	. . . 4 wff 𝑥 ∈ 𝐴
7	5, 2	wcel 2106	. . . 4 wff 𝑥 ∈ 𝐵
8	6, 7	wo 844	. . 3 wff (𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵)
9	8, 4	cab 2715	. 2 class {𝑥 ∣ (𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵)}
10	3, 9	wceq 1539	1 wff (𝐴 ∪ 𝐵) = {𝑥 ∣ (𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵)}

This definition is referenced by:  elun  4083  nfun  4099  unabw  4232  uniprg  4857  uniprOLD  4859  iinuni  5027  fvclss  7108  bnj98  32833