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Definition df-uni 4018
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 21736). This is similar to the union of two classes df-un 3327. (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 4017 . 2  class  U. A
3 vx . . . . . 6  set  x
4 vy . . . . . 6  set  y
53, 4wel 1727 . . . . 5  wff  x  e.  y
64cv 1652 . . . . . 6  class  y
76, 1wcel 1726 . . . . 5  wff  y  e.  A
85, 7wa 360 . . . 4  wff  ( x  e.  y  /\  y  e.  A )
98, 4wex 1551 . . 3  wff  E. y
( x  e.  y  /\  y  e.  A
)
109, 3cab 2424 . 2  class  { x  |  E. y ( x  e.  y  /\  y  e.  A ) }
112, 10wceq 1653 1  wff  U. A  =  { x  |  E. y ( x  e.  y  /\  y  e.  A ) }
Colors of variables: wff set class
This definition is referenced by:  dfuni2  4019  eluni  4020  csbunig  4025  unipr  4031  uniuni  4718  csbunigVD  29072
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