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Definition df-un 3170
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 20827). Contrast this operation with difference  ( A  \  B ) (df-dif 3168) and intersection  ( A  i^i  B ) (df-in 3172). For an alternate definition in terms of class difference, requiring no dummy variables, see dfun2 3417. For union defined in terms of intersection, see dfun3 3420. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
df-un  |-  ( A  u.  B )  =  { x  |  ( x  e.  A  \/  x  e.  B ) }
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 3163 . 2  class  ( A  u.  B )
4 vx . . . . . 6  set  x
54cv 1631 . . . . 5  class  x
65, 1wcel 1696 . . . 4  wff  x  e.  A
75, 2wcel 1696 . . . 4  wff  x  e.  B
86, 7wo 357 . . 3  wff  ( x  e.  A  \/  x  e.  B )
98, 4cab 2282 . 2  class  { x  |  ( x  e.  A  \/  x  e.  B ) }
103, 9wceq 1632 1  wff  ( A  u.  B )  =  { x  |  ( x  e.  A  \/  x  e.  B ) }
Colors of variables: wff set class
This definition is referenced by:  elun  3329  nfun  3344  unipr  3857  iinuni  4001  fvclss  5776  bnj98  29215
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