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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  |-  Rel USLGrph

Proof of Theorem reluslgra
Dummy variables  v 
e  x are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-uslgra 25071 . 2  |- USLGrph  =  { <. v ,  e >.  |  e : dom  e -1-1-> { x  e.  ( ~P v  \  { (/)
} )  |  (
# `  x )  <_  2 } }
21relopabi 4962 1  |-  Rel USLGrph
Colors of variables: wff setvar class
Syntax hints:   {crab 2743    \ cdif 3403   (/)c0 3733   ~Pcpw 3953   {csn 3970   class class class wbr 4405   dom cdm 4837   Rel wrel 4842   -1-1->wf1 5582   ` cfv 5585    <_ cle 9681   2c2 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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