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Definition df-sub 9277
Description: Define subtraction. Theorem subval 9281 shows its value (and describes how this definition works), theorem subaddi 9371 relates it to addition, and theorems subcli 9360 and resubcli 9347 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 9275 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8972 . . 3  class  CC
53cv 1651 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1651 . . . . . 6  class  z
8 caddc 8977 . . . . . 6  class  +
95, 7, 8co 6067 . . . . 5  class  ( y  +  z )
102cv 1651 . . . . 5  class  x
119, 10wceq 1652 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6528 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 6069 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC ( y  +  z )  =  x ) )
141, 13wceq 1652 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  9281  subf  9291
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