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Theorem relusgra 25062
 Description: The class of all undirected simple graph without loops is a relation. (Contributed by Alexander van der Vekens, 10-Aug-2017.)
Assertion
Ref Expression
relusgra USGrph

Proof of Theorem relusgra
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-usgra 25060 . 2 USGrph
21relopabi 4959 1 USGrph
 Colors of variables: wff setvar class Syntax hints:   wceq 1444  crab 2741   cdif 3401  c0 3731  cpw 3951  csn 3968   cdm 4834   wrel 4839  wf1 5579  cfv 5582  c2 10659  chash 12515   USGrph cusg 25057 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-opab 4462  df-xp 4840  df-rel 4841  df-usgra 25060 This theorem is referenced by:  usgrav  25065  elusuhgra  25095  usgrafis  25143  usgfis  39811  usgfisALT  39815
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