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Definition df-sub 9035
Description: Define subtraction. Theorem subval 9039 shows it value (and describes how this definition works), theorem subaddi 9129 relates it to addition, and theorems subcli 9118 and resubcli 9105 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 9033 . 2  class  -
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cc 8731 . . 3  class  CC
53cv 1623 . . . . . 6  class  y
6 vz . . . . . . 7  set  z
76cv 1623 . . . . . 6  class  z
8 caddc 8736 . . . . . 6  class  +
95, 7, 8co 5820 . . . . 5  class  ( y  +  z )
102cv 1623 . . . . 5  class  x
119, 10wceq 1624 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 6291 . . 3  class  ( iota_ z  e.  CC ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpt2 5822 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC ( y  +  z )  =  x ) )
141, 13wceq 1624 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  9039  subf  9049
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