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Definition df-umgra 23863
 Description: Define the class of all undirected multigraphs. A multigraph is a pair where is a 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. (Contributed by Mario Carneiro, 11-Mar-2015.)
Assertion
Ref Expression
df-umgra UMGrph
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-umgra
StepHypRef Expression
1 cumg 23860 . 2 UMGrph
2 ve . . . . . 6
32cv 1622 . . . . 5
43cdm 4689 . . . 4
5 vx . . . . . . . 8
65cv 1622 . . . . . . 7
7 chash 11337 . . . . . . 7
86, 7cfv 5255 . . . . . 6
9 c2 9795 . . . . . 6
10 cle 8868 . . . . . 6
118, 9, 10wbr 4023 . . . . 5
12 vv . . . . . . . 8
1312cv 1622 . . . . . . 7
1413cpw 3625 . . . . . 6
15 c0 3455 . . . . . . 7
1615csn 3640 . . . . . 6
1714, 16cdif 3149 . . . . 5
1811, 5, 17crab 2547 . . . 4
194, 18, 3wf 5251 . . 3
2019, 12, 2copab 4076 . 2
211, 20wceq 1623 1 UMGrph
 Colors of variables: wff set class This definition is referenced by:  relumgra  23866  isumgra  23867
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