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	⊢ 𝐴
1		cB	⊢ 𝐵
2	0 1	cun	⊢ ( 𝐴 ∪ 𝐵 )
3		vx	⊢ 𝑥
4	3	cv	⊢ 𝑥
5	4 0	wcel	⊢ 𝑥 ∈ 𝐴
6	4 1	wcel	⊢ 𝑥 ∈ 𝐵
7	5 6	wo	⊢ ( 𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵 )
8	7 3	cab	⊢ { 𝑥 ∣ ( 𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵 ) }
9	2 8	wceq	⊢ ( 𝐴 ∪ 𝐵 ) = { 𝑥 ∣ ( 𝑥 ∈ 𝐴 ∨ 𝑥 ∈ 𝐵 ) }