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Theorem grlimdmrel 47883
Description: The domain of the graph local isomorphism function is a relation. (Contributed by AV, 20-May-2025.)
Assertion
Ref Expression
grlimdmrel Rel dom GraphLocIso

Proof of Theorem grlimdmrel
Dummy variables 𝑓 𝑔 𝑣 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-grlim 47881 . 2 GraphLocIso = (𝑔 ∈ V, ∈ V ↦ {𝑓 ∣ (𝑓:(Vtx‘𝑔)–1-1-onto→(Vtx‘) ∧ ∀𝑣 ∈ (Vtx‘𝑔)(𝑔 ISubGr (𝑔 ClNeighbVtx 𝑣)) ≃𝑔𝑟 ( ISubGr ( ClNeighbVtx (𝑓𝑣))))})
21reldmmpo 7567 1 Rel dom GraphLocIso
Colors of variables: wff setvar class
Syntax hints:  wa 395  {cab 2712  wral 3059  Vcvv 3478   class class class wbr 5148  dom cdm 5689  Rel wrel 5694  1-1-ontowf1o 6562  cfv 6563  (class class class)co 7431  Vtxcvtx 29028   ClNeighbVtx cclnbgr 47743   ISubGr cisubgr 47784  𝑔𝑟 cgric 47800   GraphLocIso cgrlim 47879
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-xp 5695  df-rel 5696  df-dm 5699  df-oprab 7435  df-mpo 7436  df-grlim 47881
This theorem is referenced by:  grlimprop  47887  grlimprop2  47889  grlicrcl  47903  grilcbri2  47907
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