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Theorem relumgra 21351
 Description: The class of all undirected multigraphs is a relation. (Contributed by Mario Carneiro, 11-Mar-2015.)
Assertion
Ref Expression
relumgra UMGrph

Proof of Theorem relumgra
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-umgra 21350 . 2 UMGrph
21relopabi 5002 1 UMGrph
 Colors of variables: wff set class Syntax hints:  crab 2711   cdif 3319  c0 3630  cpw 3801  csn 3816   class class class wbr 4214   cdm 4880   wrel 4885  wf 5452  cfv 5456   cle 9123  c2 10051  chash 11620   UMGrph cumg 21349 This theorem is referenced by:  umgraf2  21354  umgrares  21361  umisuhgra  21364  umgraun  21365  vdgrun  21674  vdgrfiun  21675  iseupa  21689  eupap1  21700  eupath2lem3  21703  eupath2  21704 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269  df-xp 4886  df-rel 4887  df-umgra 21350
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