ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-sub Unicode version

Definition df-sub 7599
Description: Define subtraction. Theorem subval 7618 shows its value (and describes how this definition works), theorem subaddi 7713 relates it to addition, and theorems subcli 7702 and resubcli 7689 prove its closure laws. (Contributed by NM, 26-Nov-1994.)
Assertion
Ref Expression
df-sub  |-  -  =  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
Distinct variable group:    x, y, z

Detailed syntax breakdown of Definition df-sub
StepHypRef Expression
1 cmin 7597 . 2  class  -
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cc 7292 . . 3  class  CC
53cv 1286 . . . . . 6  class  y
6 vz . . . . . . 7  setvar  z
76cv 1286 . . . . . 6  class  z
8 caddc 7297 . . . . . 6  class  +
95, 7, 8co 5613 . . . . 5  class  ( y  +  z )
102cv 1286 . . . . 5  class  x
119, 10wceq 1287 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 5568 . . 3  class  ( iota_ z  e.  CC  ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 5615 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
141, 13wceq 1287 1  wff  -  =  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
Colors of variables: wff set class
This definition is referenced by:  subval  7618  subf  7628
  Copyright terms: Public domain W3C validator