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Definition df-div 7434
Description: Define division. Theorem divmulap 7436 relates it to multiplication, and divclap 7439 and redivclap 7489 prove its closure laws. (Contributed by NM, 2-Feb-1995.) (Revised by Mario Carneiro, 1-Apr-2014.) (New usage is discouraged.)
Assertion
Ref Expression
df-div  CC ,  CC  \  { 0 }  |->  iota_  CC  x.
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-div
StepHypRef Expression
1 cdiv 7433 . 2
2 vx . . 3  setvar
3 vy . . 3  setvar
4 cc 6709 . . 3  CC
5 cc0 6711 . . . . 5  0
65csn 3367 . . . 4  { 0 }
74, 6cdif 2908 . . 3  CC 
\  { 0 }
83cv 1241 . . . . . 6
9 vz . . . . . . 7  setvar
109cv 1241 . . . . . 6
11 cmul 6716 . . . . . 6  x.
128, 10, 11co 5455 . . . . 5  x.
132cv 1241 . . . . 5
1412, 13wceq 1242 . . . 4  x.
1514, 9, 4crio 5410 . . 3  iota_  CC  x.
162, 3, 4, 7, 15cmpt2 5457 . 2  CC ,  CC  \  { 0 } 
|->  iota_  CC  x.
171, 16wceq 1242 1  CC ,  CC  \  { 0 }  |->  iota_  CC  x.
Colors of variables: wff set class
This definition is referenced by:  divvalap  7435  divfnzn  8332
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