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Theorem relsubgr 29301
Description: The class of the subgraph relation is a relation. (Contributed by AV, 16-Nov-2020.)
Assertion
Ref Expression
relsubgr Rel SubGraph

Proof of Theorem relsubgr
Dummy variables 𝑔 𝑠 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-subgr 29300 . 2 SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
21relopabiv 5833 1 Rel SubGraph
Colors of variables: wff setvar class
Syntax hints:  w3a 1086   = wceq 1537  wss 3963  𝒫 cpw 4605  dom cdm 5689  cres 5691  Rel wrel 5694  cfv 6563  Vtxcvtx 29028  iEdgciedg 29029  Edgcedg 29079   SubGraph csubgr 29299
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-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-xp 5695  df-rel 5696  df-subgr 29300
This theorem is referenced by:  subgrv  29302
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