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Theorem relsubgr 29102
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 29101 . 2 SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
21relopabiv 5826 1 Rel SubGraph
Colors of variables: wff setvar class
Syntax hints:  w3a 1084   = wceq 1533  wss 3949  𝒫 cpw 4606  dom cdm 5682  cres 5684  Rel wrel 5687  cfv 6553  Vtxcvtx 28829  iEdgciedg 28830  Edgcedg 28880   SubGraph csubgr 29100
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3475  df-in 3956  df-ss 3966  df-opab 5215  df-xp 5688  df-rel 5689  df-subgr 29101
This theorem is referenced by:  subgrv  29103
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