Theorem relsubgr 28526

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 28525	. 2 ⊢ SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
2	1	relopabiv 5821	1 ⊢ Rel SubGraph

Syntax hints:   ∧ w3a 1088   = wceq 1542   ⊆ wss 3949  𝒫 cpw 4603  dom cdm 5677   ↾ cres 5679  Rel wrel 5682  ‘cfv 6544  Vtxcvtx 28256  iEdgciedg 28257  Edgcedg 28307   SubGraph csubgr 28524

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-opab 5212  df-xp 5683  df-rel 5684  df-subgr 28525

This theorem is referenced by:  subgrv  28527