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Definition df-div 7414
 Description: Define division. Theorem divmulap 7416 relates it to multiplication, and divclap 7419 and redivclap 7469 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 / = (x ℂ, y (ℂ ∖ {0}) ↦ (z ℂ (y · z) = x))
Distinct variable group:   x,y,z

Detailed syntax breakdown of Definition df-div
StepHypRef Expression
1 cdiv 7413 . 2 class /
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 cc 6689 . . 3 class
5 cc0 6691 . . . . 5 class 0
65csn 3367 . . . 4 class {0}
74, 6cdif 2908 . . 3 class (ℂ ∖ {0})
83cv 1241 . . . . . 6 class y
9 vz . . . . . . 7 setvar z
109cv 1241 . . . . . 6 class z
11 cmul 6696 . . . . . 6 class ·
128, 10, 11co 5455 . . . . 5 class (y · z)
132cv 1241 . . . . 5 class x
1412, 13wceq 1242 . . . 4 wff (y · z) = x
1514, 9, 4crio 5410 . . 3 class (z ℂ (y · z) = x)
162, 3, 4, 7, 15cmpt2 5457 . 2 class (x ℂ, y (ℂ ∖ {0}) ↦ (z ℂ (y · z) = x))
171, 16wceq 1242 1 wff / = (x ℂ, y (ℂ ∖ {0}) ↦ (z ℂ (y · z) = x))
 Colors of variables: wff set class This definition is referenced by:  divvalap  7415  divfnzn  8312
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