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Definition df-rtrclrec 24054
Description: The reflexive, transitive closure of a relation constructed as the union of all finite exponentiations. (Contributed by Drahflow, 12-Nov-2015.)
Assertion
Ref Expression
df-rtrclrec  |-  t
*rec  =  ( r  e.  _V  |->  U_ n  e.  NN0  ( r ^
r n ) )
Distinct variable group:    n, r

Detailed syntax breakdown of Definition df-rtrclrec
StepHypRef Expression
1 crtrcl 24053 . 2  class  t *rec
2 vr . . 3  set  r
3 cvv 2801 . . 3  class  _V
4 vn . . . 4  set  n
5 cn0 9981 . . . 4  class  NN0
62cv 1631 . . . . 5  class  r
74cv 1631 . . . . 5  class  n
8 crelexp 24038 . . . . 5  class  ^ r
96, 7, 8co 5874 . . . 4  class  ( r ^ r n )
104, 5, 9ciun 3921 . . 3  class  U_ n  e.  NN0  ( r ^
r n )
112, 3, 10cmpt 4093 . 2  class  ( r  e.  _V  |->  U_ n  e.  NN0  ( r ^
r n ) )
121, 11wceq 1632 1  wff  t
*rec  =  ( r  e.  _V  |->  U_ n  e.  NN0  ( r ^
r n ) )
Colors of variables: wff set class
This definition is referenced by:  dfrtrclrec2  24055  rtrclreclem.refl  24056  rtrclreclem.subset  24057  rtrclreclem.min  24059
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