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Theorem isomgrrel 46100
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 46099 . 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 5777 1 Rel IsomGr
Colors of variables: wff setvar class
Syntax hints:  wa 397   = wceq 1542  wex 1782  wral 3061  dom cdm 5634  cima 5637  Rel wrel 5639  1-1-ontowf1o 6496  cfv 6497  Vtxcvtx 27989  iEdgciedg 27990   IsomGr cisomgr 46097
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-in 3918  df-ss 3928  df-opab 5169  df-xp 5640  df-rel 5641  df-isomgr 46099
This theorem is referenced by:  isisomgr  46102
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