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Definition df-tc 7422
Description: The transitive closure function. (Contributed by Mario Carneiro, 23-Jun-2013.)
Assertion
Ref Expression
df-tc  |-  TC  =  ( x  e.  _V  |->  |^|
{ y  |  ( x  C_  y  /\  Tr  y ) } )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-tc
StepHypRef Expression
1 ctc 7421 . 2  class  TC
2 vx . . 3  set  x
3 cvv 2788 . . 3  class  _V
42cv 1622 . . . . . . 7  class  x
5 vy . . . . . . . 8  set  y
65cv 1622 . . . . . . 7  class  y
74, 6wss 3152 . . . . . 6  wff  x  C_  y
86wtr 4113 . . . . . 6  wff  Tr  y
97, 8wa 358 . . . . 5  wff  ( x 
C_  y  /\  Tr  y )
109, 5cab 2269 . . . 4  class  { y  |  ( x  C_  y  /\  Tr  y ) }
1110cint 3862 . . 3  class  |^| { y  |  ( x  C_  y  /\  Tr  y ) }
122, 3, 11cmpt 4077 . 2  class  ( x  e.  _V  |->  |^| { y  |  ( x  C_  y  /\  Tr  y ) } )
131, 12wceq 1623 1  wff  TC  =  ( x  e.  _V  |->  |^|
{ y  |  ( x  C_  y  /\  Tr  y ) } )
Colors of variables: wff set class
This definition is referenced by:  tcvalg  7423
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