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Mathbox for Alexander van der Vekens |
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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 46099 | . 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 5777 | 1 ⊢ Rel IsomGr |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 397 = wceq 1542 ∃wex 1782 ∀wral 3061 dom cdm 5634 “ cima 5637 Rel wrel 5639 –1-1-onto→wf1o 6496 ‘cfv 6497 Vtxcvtx 27989 iEdgciedg 27990 IsomGr cisomgr 46097 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3446 df-in 3918 df-ss 3928 df-opab 5169 df-xp 5640 df-rel 5641 df-isomgr 46099 |
This theorem is referenced by: isisomgr 46102 |
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