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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 46003 | . 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 5776 | 1 ⊢ Rel IsomGr |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 396 = wceq 1541 ∃wex 1781 ∀wral 3064 dom cdm 5633 “ cima 5636 Rel wrel 5638 –1-1-onto→wf1o 6495 ‘cfv 6496 Vtxcvtx 27947 iEdgciedg 27948 IsomGr cisomgr 46001 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3447 df-in 3917 df-ss 3927 df-opab 5168 df-xp 5639 df-rel 5640 df-isomgr 46003 |
This theorem is referenced by: isisomgr 46006 |
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