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

Definition df-gcd 12686
 Description: Define the operator. (Contributed by Paul Chapman, 21-Mar-2011.)
Assertion
Ref Expression
df-gcd
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-gcd
StepHypRef Expression
1 cgcd 12685 . 2
2 vx . . 3
3 vy . . 3
4 cz 10024 . . 3
52cv 1622 . . . . . 6
6 cc0 8737 . . . . . 6
75, 6wceq 1623 . . . . 5
83cv 1622 . . . . . 6
98, 6wceq 1623 . . . . 5
107, 9wa 358 . . . 4
11 vn . . . . . . . . 9
1211cv 1622 . . . . . . . 8
13 cdivides 12531 . . . . . . . 8
1412, 5, 13wbr 4023 . . . . . . 7
1512, 8, 13wbr 4023 . . . . . . 7
1614, 15wa 358 . . . . . 6
1716, 11, 4crab 2547 . . . . 5
18 cr 8736 . . . . 5
19 clt 8867 . . . . 5
2017, 18, 19csup 7193 . . . 4
2110, 6, 20cif 3565 . . 3
222, 3, 4, 4, 21cmpt2 5860 . 2
231, 22wceq 1623 1
 Colors of variables: wff set class This definition is referenced by:  gcdval  12687  gcdf  12698
 Copyright terms: Public domain W3C validator