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Definition df-sub 8126
Description: Define subtraction. Theorem subval 8145 shows its value (and describes how this definition works), Theorem subaddi 8240 relates it to addition, and Theorems subcli 8229 and resubcli 8216 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 8124 . 2  class  -
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cc 7806 . . 3  class  CC
53cv 1352 . . . . . 6  class  y
6 vz . . . . . . 7  setvar  z
76cv 1352 . . . . . 6  class  z
8 caddc 7811 . . . . . 6  class  +
95, 7, 8co 5872 . . . . 5  class  ( y  +  z )
102cv 1352 . . . . 5  class  x
119, 10wceq 1353 . . . 4  wff  ( y  +  z )  =  x
1211, 6, 4crio 5827 . . 3  class  ( iota_ z  e.  CC  ( y  +  z )  =  x )
132, 3, 4, 4, 12cmpo 5874 . 2  class  ( x  e.  CC ,  y  e.  CC  |->  ( iota_ z  e.  CC  ( y  +  z )  =  x ) )
141, 13wceq 1353 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  8145  subf  8155
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