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

Definition df-evl 17411
Description: A simplification of evalSub when the evaluation ring is the same as the coefficient ring. (Contributed by Stefan O'Rear, 19-Mar-2015.)
Assertion
Ref Expression
df-evl  |- eval  =  ( i  e.  _V , 
r  e.  _V  |->  ( ( i evalSub  r ) `
 ( Base `  r
) ) )
Distinct variable group:    i, r

Detailed syntax breakdown of Definition df-evl
StepHypRef Expression
1 cevl 17400 . 2  class eval
2 vi . . 3  setvar  i
3 vr . . 3  setvar  r
4 cvv 2970 . . 3  class  _V
53cv 1363 . . . . 5  class  r
6 cbs 14170 . . . . 5  class  Base
75, 6cfv 5415 . . . 4  class  ( Base `  r )
82cv 1363 . . . . 5  class  i
9 ces 17399 . . . . 5  class evalSub
108, 5, 9co 6090 . . . 4  class  ( i evalSub 
r )
117, 10cfv 5415 . . 3  class  ( ( i evalSub  r ) `  ( Base `  r )
)
122, 3, 4, 4, 11cmpt2 6092 . 2  class  ( i  e.  _V ,  r  e.  _V  |->  ( ( i evalSub  r ) `  ( Base `  r )
) )
131, 12wceq 1364 1  wff eval  =  ( i  e.  _V , 
r  e.  _V  |->  ( ( i evalSub  r ) `
 ( Base `  r
) ) )
Colors of variables: wff setvar class
This definition is referenced by:  evlval  21434  evl1fval  21436  mzpmfp  28992  mzpmfpOLD  28993
  Copyright terms: Public domain W3C validator