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| Description: The class of the subgraph relation is a relation. (Contributed by AV, 16-Nov-2020.) | 
| Ref | Expression | 
|---|---|
| relsubgr | ⊢ Rel SubGraph | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-subgr 29286 | . 2 ⊢ SubGraph = {〈𝑠, 𝑔〉 ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))} | |
| 2 | 1 | relopabiv 5829 | 1 ⊢ Rel SubGraph | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∧ w3a 1086 = wceq 1539 ⊆ wss 3950 𝒫 cpw 4599 dom cdm 5684 ↾ cres 5686 Rel wrel 5689 ‘cfv 6560 Vtxcvtx 29014 iEdgciedg 29015 Edgcedg 29065 SubGraph csubgr 29285 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1542 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-ss 3967 df-opab 5205 df-xp 5690 df-rel 5691 df-subgr 29286 | 
| This theorem is referenced by: subgrv 29288 | 
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