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Mirrors > Home > MPE Home > Th. List > relsubgr | Structured version Visualization version GIF version |
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 29300 | . 2 ⊢ SubGraph = {〈𝑠, 𝑔〉 ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))} | |
2 | 1 | relopabiv 5833 | 1 ⊢ Rel SubGraph |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1086 = wceq 1537 ⊆ wss 3963 𝒫 cpw 4605 dom cdm 5689 ↾ cres 5691 Rel wrel 5694 ‘cfv 6563 Vtxcvtx 29028 iEdgciedg 29029 Edgcedg 29079 SubGraph csubgr 29299 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-ss 3980 df-opab 5211 df-xp 5695 df-rel 5696 df-subgr 29300 |
This theorem is referenced by: subgrv 29302 |
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