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Theorem reluslgra 25073
 Description: The class of all undirected simple graph with loops is a relation. (Contributed by Alexander van der Vekens, 10-Aug-2017.)
Assertion
Ref Expression
reluslgra USLGrph

Proof of Theorem reluslgra
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-uslgra 25071 . 2 USLGrph
21relopabi 4962 1 USLGrph
 Colors of variables: wff setvar class Syntax hints:  crab 2743   cdif 3403  c0 3733  cpw 3953  csn 3970   class class class wbr 4405   cdm 4837   wrel 4842  wf1 5582  cfv 5585   cle 9681  c2 10666  chash 12522   USLGrph cuslg 25068 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-9 1898  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433  ax-sep 4528  ax-nul 4537  ax-pr 4642 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3734  df-if 3884  df-sn 3971  df-pr 3973  df-op 3977  df-opab 4465  df-xp 4843  df-rel 4844  df-uslgra 25071 This theorem is referenced by:  uslgrav  25076  uslgraf  25084
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