![]() |
Mathbox for Alexander van der Vekens |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > isomgrrel | Structured version Visualization version GIF version |
Description: The isomorphy relation for graphs is a relation. (Contributed by AV, 11-Nov-2022.) |
Ref | Expression |
---|---|
isomgrrel | ⊢ Rel IsomGr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-isomgr 46789 | . 2 ⊢ IsomGr = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓(𝑓:(Vtx‘𝑥)–1-1-onto→(Vtx‘𝑦) ∧ ∃𝑔(𝑔:dom (iEdg‘𝑥)–1-1-onto→dom (iEdg‘𝑦) ∧ ∀𝑖 ∈ dom (iEdg‘𝑥)(𝑓 “ ((iEdg‘𝑥)‘𝑖)) = ((iEdg‘𝑦)‘(𝑔‘𝑖))))} | |
2 | 1 | relopabiv 5821 | 1 ⊢ Rel IsomGr |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 395 = wceq 1540 ∃wex 1780 ∀wral 3060 dom cdm 5677 “ cima 5680 Rel wrel 5682 –1-1-onto→wf1o 6543 ‘cfv 6544 Vtxcvtx 28520 iEdgciedg 28521 IsomGr cisomgr 46787 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 df-in 3956 df-ss 3966 df-opab 5212 df-xp 5683 df-rel 5684 df-isomgr 46789 |
This theorem is referenced by: isisomgr 46792 |
Copyright terms: Public domain | W3C validator |