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Definition df-umgra 21340
 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 21339 . 2 UMGrph
2 ve . . . . . 6
32cv 1651 . . . . 5
43cdm 4870 . . . 4
5 vx . . . . . . . 8
65cv 1651 . . . . . . 7
7 chash 11610 . . . . . . 7
86, 7cfv 5446 . . . . . 6
9 c2 10041 . . . . . 6
10 cle 9113 . . . . . 6
118, 9, 10wbr 4204 . . . . 5
12 vv . . . . . . . 8
1312cv 1651 . . . . . . 7
1413cpw 3791 . . . . . 6
15 c0 3620 . . . . . . 7
1615csn 3806 . . . . . 6
1714, 16cdif 3309 . . . . 5
1811, 5, 17crab 2701 . . . 4
194, 18, 3wf 5442 . . 3
2019, 12, 2copab 4257 . 2
211, 20wceq 1652 1 UMGrph
 Colors of variables: wff set class This definition is referenced by:  relumgra  21341  isumgra  21342
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