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Theorem relsubgr 27062
 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 27061 . 2 SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
21relopabi 5662 1 Rel SubGraph
 Colors of variables: wff setvar class Syntax hints:   ∧ w3a 1084   = wceq 1538   ⊆ wss 3884  𝒫 cpw 4500  dom cdm 5523   ↾ cres 5525  Rel wrel 5528  ‘cfv 6328  Vtxcvtx 26792  iEdgciedg 26793  Edgcedg 26843   SubGraph csubgr 27060 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 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-11 2159  ax-12 2176  ax-ext 2773 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-sn 4529  df-pr 4531  df-op 4535  df-opab 5096  df-xp 5529  df-rel 5530  df-subgr 27061 This theorem is referenced by:  subgrv  27063
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