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

Definition df-ef 12633
Description: Define the exponential function. (Contributed by NM, 14-Mar-2005.)
Assertion
Ref Expression
df-ef  |-  exp  =  ( x  e.  CC  |->  sum_ k  e.  NN0  (
( x ^ k
)  /  ( ! `
 k ) ) )
Distinct variable group:    x, k

Detailed syntax breakdown of Definition df-ef
StepHypRef Expression
1 ce 12627 . 2  class  exp
2 vx . . 3  set  x
3 cc 8952 . . 3  class  CC
4 cn0 10185 . . . 4  class  NN0
52cv 1648 . . . . . 6  class  x
6 vk . . . . . . 7  set  k
76cv 1648 . . . . . 6  class  k
8 cexp 11345 . . . . . 6  class  ^
95, 7, 8co 6048 . . . . 5  class  ( x ^ k )
10 cfa 11529 . . . . . 6  class  !
117, 10cfv 5421 . . . . 5  class  ( ! `
 k )
12 cdiv 9641 . . . . 5  class  /
139, 11, 12co 6048 . . . 4  class  ( ( x ^ k )  /  ( ! `  k ) )
144, 13, 6csu 12442 . . 3  class  sum_ k  e.  NN0  ( ( x ^ k )  / 
( ! `  k
) )
152, 3, 14cmpt 4234 . 2  class  ( x  e.  CC  |->  sum_ k  e.  NN0  ( ( x ^ k )  / 
( ! `  k
) ) )
161, 15wceq 1649 1  wff  exp  =  ( x  e.  CC  |->  sum_ k  e.  NN0  (
( x ^ k
)  /  ( ! `
 k ) ) )
Colors of variables: wff set class
This definition is referenced by:  efval  12645  eff  12647
  Copyright terms: Public domain W3C validator