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Theorem isomgrrel 46004
Description: The isomorphy relation for graphs is a relation. (Contributed by AV, 11-Nov-2022.)
Assertion
Ref Expression
isomgrrel Rel IsomGr

Proof of Theorem isomgrrel
Dummy variables 𝑓 𝑔 𝑖 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-isomgr 46003 . 2 IsomGr = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓(𝑓:(Vtx‘𝑥)–1-1-onto→(Vtx‘𝑦) ∧ ∃𝑔(𝑔:dom (iEdg‘𝑥)–1-1-onto→dom (iEdg‘𝑦) ∧ ∀𝑖 ∈ dom (iEdg‘𝑥)(𝑓 “ ((iEdg‘𝑥)‘𝑖)) = ((iEdg‘𝑦)‘(𝑔𝑖))))}
21relopabiv 5776 1 Rel IsomGr
Colors of variables: wff setvar class
Syntax hints:  wa 396   = wceq 1541  wex 1781  wral 3064  dom cdm 5633  cima 5636  Rel wrel 5638  1-1-ontowf1o 6495  cfv 6496  Vtxcvtx 27947  iEdgciedg 27948   IsomGr cisomgr 46001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3447  df-in 3917  df-ss 3927  df-opab 5168  df-xp 5639  df-rel 5640  df-isomgr 46003
This theorem is referenced by:  isisomgr  46006
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