Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-div Structured version   Unicode version

Definition df-div 9683
 Description: Define division. Theorem divmuli 9773 relates it to multiplication, and divcli 9761 and redivcli 9786 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
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-div
StepHypRef Expression
1 cdiv 9682 . 2
2 vx . . 3
3 vy . . 3
4 cc 8993 . . 3
5 cc0 8995 . . . . 5
65csn 3816 . . . 4
74, 6cdif 3319 . . 3
83cv 1652 . . . . . 6
9 vz . . . . . . 7
109cv 1652 . . . . . 6
11 cmul 9000 . . . . . 6
128, 10, 11co 6084 . . . . 5
132cv 1652 . . . . 5
1412, 13wceq 1653 . . . 4
1514, 9, 4crio 6545 . . 3
162, 3, 4, 7, 15cmpt2 6086 . 2
171, 16wceq 1653 1
 Colors of variables: wff set class This definition is referenced by:  1div0  9684  divval  9685  elq  10581  cnflddiv  16736  divcn  18903  1div0apr  21767
 Copyright terms: Public domain W3C validator