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Definition df-uni 4191
Description: Define the union of a class i.e. the collection of all members of the members of the class. Definition 5.5 of [TakeutiZaring] p. 16. For example,  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  {
1 ,  3 ,  8 } (ex-uni 25445). This is similar to the union of two classes df-un 3418. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
df-uni  |-  U. A  =  { x  |  E. y ( x  e.  y  /\  y  e.  A ) }
Distinct variable group:    x, y, A

Detailed syntax breakdown of Definition df-uni
StepHypRef Expression
1 cA . . 3  class  A
21cuni 4190 . 2  class  U. A
3 vx . . . . . 6  setvar  x
4 vy . . . . . 6  setvar  y
53, 4wel 1843 . . . . 5  wff  x  e.  y
64cv 1404 . . . . . 6  class  y
76, 1wcel 1842 . . . . 5  wff  y  e.  A
85, 7wa 367 . . . 4  wff  ( x  e.  y  /\  y  e.  A )
98, 4wex 1633 . . 3  wff  E. y
( x  e.  y  /\  y  e.  A
)
109, 3cab 2387 . 2  class  { x  |  E. y ( x  e.  y  /\  y  e.  A ) }
112, 10wceq 1405 1  wff  U. A  =  { x  |  E. y ( x  e.  y  /\  y  e.  A ) }
Colors of variables: wff setvar class
This definition is referenced by:  dfuni2  4192  eluni  4193  unipr  4203  csbuni  4218  uniuni  6547  csbunigOLD  36627  csbunigVD  36710
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