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Mirrors > Home > MPE Home > Th. List > Mathboxes > 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 40492 | . 2 ⊢ SubGraph = {〈𝑠, 𝑔〉 ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))} | |
2 | 1 | relopabi 5167 | 1 ⊢ Rel SubGraph |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1031 = wceq 1475 ⊆ wss 3540 𝒫 cpw 4108 dom cdm 5038 ↾ cres 5040 Rel wrel 5043 ‘cfv 5804 Vtxcvtx 25673 iEdgciedg 25674 Edgcedga 25792 SubGraph csubgr 40491 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-opab 4644 df-xp 5044 df-rel 5045 df-subgr 40492 |
This theorem is referenced by: subgrv 40494 |
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