MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ida Unicode version

Definition df-ida 13903
Description: Definition of the identity arrow, which is just the identity morphism tagged with its domain and codomain. (Contributed by FL, 26-Oct-2007.) (Revised by Mario Carneiro, 11-Jan-2017.)
Assertion
Ref Expression
df-ida  |- Ida  =  ( c  e.  Cat  |->  ( x  e.  ( Base `  c
)  |->  <. x ,  x ,  ( ( Id
`  c ) `  x ) >. )
)
Distinct variable group:    x, c

Detailed syntax breakdown of Definition df-ida
StepHypRef Expression
1 cida 13901 . 2  class Ida
2 vc . . 3  set  c
3 ccat 13582 . . 3  class  Cat
4 vx . . . 4  set  x
52cv 1631 . . . . 5  class  c
6 cbs 13164 . . . . 5  class  Base
75, 6cfv 5271 . . . 4  class  ( Base `  c )
84cv 1631 . . . . 5  class  x
9 ccid 13583 . . . . . . 7  class  Id
105, 9cfv 5271 . . . . . 6  class  ( Id
`  c )
118, 10cfv 5271 . . . . 5  class  ( ( Id `  c ) `
 x )
128, 8, 11cotp 3657 . . . 4  class  <. x ,  x ,  ( ( Id `  c ) `
 x ) >.
134, 7, 12cmpt 4093 . . 3  class  ( x  e.  ( Base `  c
)  |->  <. x ,  x ,  ( ( Id
`  c ) `  x ) >. )
142, 3, 13cmpt 4093 . 2  class  ( c  e.  Cat  |->  ( x  e.  ( Base `  c
)  |->  <. x ,  x ,  ( ( Id
`  c ) `  x ) >. )
)
151, 14wceq 1632 1  wff Ida  =  ( c  e.  Cat  |->  ( x  e.  ( Base `  c
)  |->  <. x ,  x ,  ( ( Id
`  c ) `  x ) >. )
)
Colors of variables: wff set class
This definition is referenced by:  idafval  13905
  Copyright terms: Public domain W3C validator