| Mathbox for Alexander van der Vekens |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > grlimdmrel | Structured version Visualization version GIF version | ||
| Description: The domain of the graph local isomorphism function is a relation. (Contributed by AV, 20-May-2025.) |
| Ref | Expression |
|---|---|
| grlimdmrel | ⊢ Rel dom GraphLocIso |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-grlim 47945 | . 2 ⊢ GraphLocIso = (𝑔 ∈ V, ℎ ∈ V ↦ {𝑓 ∣ (𝑓:(Vtx‘𝑔)–1-1-onto→(Vtx‘ℎ) ∧ ∀𝑣 ∈ (Vtx‘𝑔)(𝑔 ISubGr (𝑔 ClNeighbVtx 𝑣)) ≃𝑔𝑟 (ℎ ISubGr (ℎ ClNeighbVtx (𝑓‘𝑣))))}) | |
| 2 | 1 | reldmmpo 7567 | 1 ⊢ Rel dom GraphLocIso |
| Colors of variables: wff setvar class |
| Syntax hints: ∧ wa 395 {cab 2714 ∀wral 3061 Vcvv 3480 class class class wbr 5143 dom cdm 5685 Rel wrel 5690 –1-1-onto→wf1o 6560 ‘cfv 6561 (class class class)co 7431 Vtxcvtx 29013 ClNeighbVtx cclnbgr 47805 ISubGr cisubgr 47846 ≃𝑔𝑟 cgric 47862 GraphLocIso cgrlim 47943 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-br 5144 df-opab 5206 df-xp 5691 df-rel 5692 df-dm 5695 df-oprab 7435 df-mpo 7436 df-grlim 47945 |
| This theorem is referenced by: grlimprop 47951 grlimprop2 47953 grlicrcl 47967 grilcbri2 47971 |
| Copyright terms: Public domain | W3C validator |