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Definition df-sub 9249
Description: Define subtraction. Theorem subval 9253 shows its value (and describes how this definition works), theorem subaddi 9343 relates it to addition, and theorems subcli 9332 and resubcli 9319 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 9247 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8944 . . 3  class  CC
53cv 1648 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1648 . . . . . 6  class  z
8 caddc 8949 . . . . . 6  class  +
95, 7, 8co 6040 . . . . 5  class  ( y  +  z )
102cv 1648 . . . . 5  class  x
119, 10wceq 1649 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6501 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 6042 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC ( y  +  z )  =  x ) )
141, 13wceq 1649 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  9253  subf  9263
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