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Definition df-sub 9039
Description: Define subtraction. Theorem subval 9043 shows it value (and describes how this definition works), theorem subaddi 9133 relates it to addition, and theorems subcli 9122 and resubcli 9109 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 9037 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8735 . . 3  class  CC
53cv 1622 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1622 . . . . . 6  class  z
8 caddc 8740 . . . . . 6  class  +
95, 7, 8co 5858 . . . . 5  class  ( y  +  z )
102cv 1622 . . . . 5  class  x
119, 10wceq 1623 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6297 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 5860 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC ( y  +  z )  =  x ) )
141, 13wceq 1623 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  9043  subf  9053
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