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Definition df-sub 7418
Description: Define subtraction. Theorem subval 7437 shows its value (and describes how this definition works), theorem subaddi 7532 relates it to addition, and theorems subcli 7521 and resubcli 7508 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 7416 . 2  class  -
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cc 7111 . . 3  class  CC
53cv 1284 . . . . . 6  class  y
6 vz . . . . . . 7  setvar  z
76cv 1284 . . . . . 6  class  z
8 caddc 7116 . . . . . 6  class  +
95, 7, 8co 5564 . . . . 5  class  ( y  +  z )
102cv 1284 . . . . 5  class  x
119, 10wceq 1285 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 5519 . . 3  class  ( iota_ z  e.  CC  ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 5566 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
141, 13wceq 1285 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  7437  subf  7447
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