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Definition df-cmet 19163
 Description: Define the class of complete metrics. (Contributed by Mario Carneiro, 1-May-2014.)
Assertion
Ref Expression
df-cmet CauFil
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-cmet
StepHypRef Expression
1 cms 19160 . 2
2 vx . . 3
3 cvv 2916 . . 3
4 vd . . . . . . . . 9
54cv 1648 . . . . . . . 8
6 cmopn 16646 . . . . . . . 8
75, 6cfv 5413 . . . . . . 7
8 vf . . . . . . . 8
98cv 1648 . . . . . . 7
10 cflim 17919 . . . . . . 7
117, 9, 10co 6040 . . . . . 6
12 c0 3588 . . . . . 6
1311, 12wne 2567 . . . . 5
14 ccfil 19158 . . . . . 6 CauFil
155, 14cfv 5413 . . . . 5 CauFil
1613, 8, 15wral 2666 . . . 4 CauFil
172cv 1648 . . . . 5
18 cme 16642 . . . . 5
1917, 18cfv 5413 . . . 4
2016, 4, 19crab 2670 . . 3 CauFil
212, 3, 20cmpt 4226 . 2 CauFil
221, 21wceq 1649 1 CauFil
 Colors of variables: wff set class This definition is referenced by:  iscmet  19190
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