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Definition df-sub 9084
Description: Define subtraction. Theorem subval 9088 shows its value (and describes how this definition works), theorem subaddi 9178 relates it to addition, and theorems subcli 9167 and resubcli 9154 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 9082 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8780 . . 3  class  CC
53cv 1632 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1632 . . . . . 6  class  z
8 caddc 8785 . . . . . 6  class  +
95, 7, 8co 5900 . . . . 5  class  ( y  +  z )
102cv 1632 . . . . 5  class  x
119, 10wceq 1633 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6339 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 5902 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC ( y  +  z )  =  x ) )
141, 13wceq 1633 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  9088  subf  9098
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