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Definition df-sub 8043
Description: Define subtraction. Theorem subval 8062 shows its value (and describes how this definition works), Theorem subaddi 8157 relates it to addition, and Theorems subcli 8146 and resubcli 8133 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 8041 . 2  class  -
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cc 7725 . . 3  class  CC
53cv 1334 . . . . . 6  class  y
6 vz . . . . . . 7  setvar  z
76cv 1334 . . . . . 6  class  z
8 caddc 7730 . . . . . 6  class  +
95, 7, 8co 5821 . . . . 5  class  ( y  +  z )
102cv 1334 . . . . 5  class  x
119, 10wceq 1335 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 5776 . . 3  class  ( iota_ z  e.  CC  ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpo 5823 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
141, 13wceq 1335 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  8062  subf  8072
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