Theorem relsubgr 29560

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.

Step	Hyp	Ref	Expression
1		df-subgr 29559	. 2 ⊢ SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
2	1	relopabiv 5808	1 ⊢ Rel SubGraph

Syntax hints:   ∧ w3a 1101   = wceq 1567   ⊆ wss 3911  𝒫 cpw 4565  dom cdm 5662   ↾ cres 5664  Rel wrel 5667  ‘cfv 6537  Vtxcvtx 29287  iEdgciedg 29288  Edgcedg 29338   SubGraph csubgr 29558

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3463  df-ss 3928  df-opab 5176  df-xp 5668  df-rel 5669  df-subgr 29559

This theorem is referenced by:  subgrv  29561