Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-xmet Unicode version

Definition df-xmet 12194
 Description: Define the set of all extended metrics on a given base set. The definition is similar to df-met 12195, but we also allow the metric to take on the value . (Contributed by Mario Carneiro, 20-Aug-2015.)
Assertion
Ref Expression
df-xmet
Distinct variable group:   ,,,,

Detailed syntax breakdown of Definition df-xmet
StepHypRef Expression
1 cxmet 12186 . 2
2 vx . . 3
3 cvv 2689 . . 3
4 vy . . . . . . . . . . 11
54cv 1331 . . . . . . . . . 10
6 vz . . . . . . . . . . 11
76cv 1331 . . . . . . . . . 10
8 vd . . . . . . . . . . 11
98cv 1331 . . . . . . . . . 10
105, 7, 9co 5781 . . . . . . . . 9
11 cc0 7643 . . . . . . . . 9
1210, 11wceq 1332 . . . . . . . 8
134, 6weq 1480 . . . . . . . 8
1412, 13wb 104 . . . . . . 7
15 vw . . . . . . . . . . . 12
1615cv 1331 . . . . . . . . . . 11
1716, 5, 9co 5781 . . . . . . . . . 10
1816, 7, 9co 5781 . . . . . . . . . 10
19 cxad 9586 . . . . . . . . . 10
2017, 18, 19co 5781 . . . . . . . . 9
21 cle 7824 . . . . . . . . 9
2210, 20, 21wbr 3936 . . . . . . . 8
232cv 1331 . . . . . . . 8
2422, 15, 23wral 2417 . . . . . . 7
2514, 24wa 103 . . . . . 6
2625, 6, 23wral 2417 . . . . 5
2726, 4, 23wral 2417 . . . 4
28 cxr 7822 . . . . 5
2923, 23cxp 4544 . . . . 5
30 cmap 6549 . . . . 5
3128, 29, 30co 5781 . . . 4
3227, 8, 31crab 2421 . . 3
332, 3, 32cmpt 3996 . 2
341, 33wceq 1332 1
 Colors of variables: wff set class This definition is referenced by:  xmetrel  12549  isxmet  12551  xmetf  12556  xmetunirn  12564
 Copyright terms: Public domain W3C validator