Definition df-un 2102

Description: Define the union of two classes. Definition 5.6 of [TakeutiZaring] p. 16. For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 2295. For union defined in terms of intersection, see dfun3 2298.

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 2097	. 2 class (A ∪ B)
4		vx	. . . . . 6 set x
5	4	cv 991	. . . . 5 class x
6	5, 1	wcel 994	. . . 4 wff x ∈ A
7	5, 2	wcel 994	. . . 4 wff x ∈ B
8	6, 7	wo 220	. . 3 wff (x ∈ A ⋁ x ∈ B)
9	8, 4	cab 1505	. 2 class {x∣(x ∈ A ⋁ x ∈ B)}
10	3, 9	wceq 992	1 wff (A ∪ B) = {x∣(x ∈ A ⋁ x ∈ B)}

This definition is referenced by:  elun 2225  ssequn1 2252  unipr 2581  fvclss 3969

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