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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  |-  Rel UMGrph

Proof of Theorem relumgra
Dummy variables  e 
v  x are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-umgra 21350 . 2  |- UMGrph  =  { <. v ,  e >.  |  e : dom  e
--> { x  e.  ( ~P v  \  { (/)
} )  |  (
# `  x )  <_  2 } }
21relopabi 5002 1  |-  Rel UMGrph
Colors of variables: wff set class
Syntax hints:   {crab 2711    \ cdif 3319   (/)c0 3630   ~Pcpw 3801   {csn 3816   class class class wbr 4214   dom cdm 4880   Rel wrel 4885   -->wf 5452   ` cfv 5456    <_ cle 9123   2c2 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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