Theorem relsubgr 29472

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 29471	. 2 ⊢ SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
2	1	relopabiv 5795	1 ⊢ Rel SubGraph

Syntax hints:   ∧ w3a 1099   = wceq 1562   ⊆ wss 3906  𝒫 cpw 4557  dom cdm 5649   ↾ cres 5651  Rel wrel 5654  ‘cfv 6523  Vtxcvtx 29199  iEdgciedg 29200  Edgcedg 29250   SubGraph csubgr 29470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1565  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-v 3458  df-ss 3923  df-opab 5165  df-xp 5655  df-rel 5656  df-subgr 29471

This theorem is referenced by:  subgrv  29473