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

Definition df-uslgra 25059
 Description: Define the class of all undirected simple graphs with loops. An undirected simple graph with loops is a special undirected multigraph where is an injective (one-to-one) function into subsets of of cardinality one or two, representing the two vertices incident to the edge, or the one vertex if the edge is a loop. In contrast to a multigraph, there is at most one edge between two vertices. (Contributed by Alexander van der Vekens, 10-Aug-2017.)
Assertion
Ref Expression
df-uslgra USLGrph
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-uslgra
StepHypRef Expression
1 cuslg 25056 . 2 USLGrph
2 ve . . . . . 6
32cv 1443 . . . . 5
43cdm 4834 . . . 4
5 vx . . . . . . . 8
65cv 1443 . . . . . . 7
7 chash 12515 . . . . . . 7
86, 7cfv 5582 . . . . . 6
9 c2 10659 . . . . . 6
10 cle 9676 . . . . . 6
118, 9, 10wbr 4402 . . . . 5
12 vv . . . . . . . 8
1312cv 1443 . . . . . . 7
1413cpw 3951 . . . . . 6
15 c0 3731 . . . . . . 7
1615csn 3968 . . . . . 6
1714, 16cdif 3401 . . . . 5
1811, 5, 17crab 2741 . . . 4
194, 18, 3wf1 5579 . . 3
2019, 12, 2copab 4460 . 2
211, 20wceq 1444 1 USLGrph
 Colors of variables: wff setvar class This definition is referenced by:  reluslgra  25061  isuslgra  25070
 Copyright terms: Public domain W3C validator