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Definition df-sub 7903
Description: Define subtraction. Theorem subval 7922 shows its value (and describes how this definition works), theorem subaddi 8017 relates it to addition, and theorems subcli 8006 and resubcli 7993 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 7901 . 2  class  -
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cc 7586 . . 3  class  CC
53cv 1315 . . . . . 6  class  y
6 vz . . . . . . 7  setvar  z
76cv 1315 . . . . . 6  class  z
8 caddc 7591 . . . . . 6  class  +
95, 7, 8co 5742 . . . . 5  class  ( y  +  z )
102cv 1315 . . . . 5  class  x
119, 10wceq 1316 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 5697 . . 3  class  ( iota_ z  e.  CC  ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpo 5744 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
141, 13wceq 1316 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  7922  subf  7932
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