Theorem relsubgr 29356

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 29355	. 2 ⊢ SubGraph = {⟨𝑠, 𝑔⟩ ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))}
2	1	relopabiv 5771	1 ⊢ Rel SubGraph

Syntax hints:   ∧ w3a 1087   = wceq 1542   ⊆ wss 3890  𝒫 cpw 4542  dom cdm 5626   ↾ cres 5628  Rel wrel 5631  ‘cfv 6494  Vtxcvtx 29083  iEdgciedg 29084  Edgcedg 29134   SubGraph csubgr 29354

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-ss 3907  df-opab 5149  df-xp 5632  df-rel 5633  df-subgr 29355

This theorem is referenced by:  subgrv  29357