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Metamath Proof Explorer

Definition df-un

Description: Define the union of two classes. Definition 5.6 of TakeutiZaring p. 16. For example, ( { 1 , 3 } u. { 1 , 8 } ) = { 1 , 3 , 8 } ( ex-un ). Contrast this operation with difference ( A \ B ) ( df-dif ) and intersection ( A i^i B ) ( df-in ). For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 . For union defined in terms of intersection, see dfun3 . (Contributed by NM, 23-Aug-1993)

Ref Expression
Assertion df-un ⊢ A ∪ B = x | x ∈ A ∨ x ∈ B

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA class A
1 cB class B
2 0 1 cun class A ∪ B
3 vx setvar x
4 3 cv setvar x
5 4 0 wcel wff x ∈ A
6 4 1 wcel wff x ∈ B
7 5 6 wo wff x ∈ A ∨ x ∈ B
8 7 3 cab class x | x ∈ A ∨ x ∈ B
9 2 8 wceq wff A ∪ B = x | x ∈ A ∨ x ∈ B