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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 26160 | . 2 ⊢ SubGraph = {〈𝑠, 𝑔〉 ∣ ((Vtx‘𝑠) ⊆ (Vtx‘𝑔) ∧ (iEdg‘𝑠) = ((iEdg‘𝑔) ↾ dom (iEdg‘𝑠)) ∧ (Edg‘𝑠) ⊆ 𝒫 (Vtx‘𝑠))} | |
2 | 1 | relopabi 5245 | 1 ⊢ Rel SubGraph |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1037 = wceq 1483 ⊆ wss 3574 𝒫 cpw 4158 dom cdm 5114 ↾ cres 5116 Rel wrel 5119 ‘cfv 5888 Vtxcvtx 25874 iEdgciedg 25875 Edgcedg 25939 SubGraph csubgr 26159 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-opab 4713 df-xp 5120 df-rel 5121 df-subgr 26160 |
This theorem is referenced by: subgrv 26162 |
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