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Definition df-sub 9295
Description: Define subtraction. Theorem subval 9299 shows its value (and describes how this definition works), theorem subaddi 9389 relates it to addition, and theorems subcli 9378 and resubcli 9365 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 9293 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8990 . . 3  class  CC
53cv 1652 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1652 . . . . . 6  class  z
8 caddc 8995 . . . . . 6  class  +
95, 7, 8co 6083 . . . . 5  class  ( y  +  z )
102cv 1652 . . . . 5  class  x
119, 10wceq 1653 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6544 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 6085 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC ( y  +  z )  =  x ) )
141, 13wceq 1653 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  9299  subf  9309
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