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Definition df-sub 7246
Description: Define subtraction. Theorem subval 7265 shows its value (and describes how this definition works), theorem subaddi 7360 relates it to addition, and theorems subcli 7349 and resubcli 7336 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 7244 . 2  class  -
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cc 6944 . . 3  class  CC
53cv 1258 . . . . . 6  class  y
6 vz . . . . . . 7  setvar  z
76cv 1258 . . . . . 6  class  z
8 caddc 6949 . . . . . 6  class  +
95, 7, 8co 5539 . . . . 5  class  ( y  +  z )
102cv 1258 . . . . 5  class  x
119, 10wceq 1259 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 5494 . . 3  class  ( iota_ z  e.  CC  ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 5541 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
141, 13wceq 1259 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  7265  subf  7275
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