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Definition df-sub 9227
Description: Define subtraction. Theorem subval 9231 shows its value (and describes how this definition works), theorem subaddi 9321 relates it to addition, and theorems subcli 9310 and resubcli 9297 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 9225 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8923 . . 3  class  CC
53cv 1648 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1648 . . . . . 6  class  z
8 caddc 8928 . . . . . 6  class  +
95, 7, 8co 6022 . . . . 5  class  ( y  +  z )
102cv 1648 . . . . 5  class  x
119, 10wceq 1649 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6480 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 6024 . 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  9231  subf  9241
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