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Theorem relsubgr 29287
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 29286 . 2 SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
21relopabiv 5829 1 Rel SubGraph
Colors of variables: wff setvar class
Syntax hints:  w3a 1086   = wceq 1539  wss 3950  𝒫 cpw 4599  dom cdm 5684  cres 5686  Rel wrel 5689  cfv 6560  Vtxcvtx 29014  iEdgciedg 29015  Edgcedg 29065   SubGraph csubgr 29285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-ss 3967  df-opab 5205  df-xp 5690  df-rel 5691  df-subgr 29286
This theorem is referenced by:  subgrv  29288
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