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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 44060 | . 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 | relopabi 5687 | 1 ⊢ Rel IsomGr |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 = wceq 1536 ∃wex 1779 ∀wral 3137 dom cdm 5548 “ cima 5551 Rel wrel 5553 –1-1-onto→wf1o 6347 ‘cfv 6348 Vtxcvtx 26779 iEdgciedg 26780 IsomGr cisomgr 44058 |
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 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1084 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-rab 3146 df-v 3493 df-dif 3932 df-un 3934 df-in 3936 df-ss 3945 df-nul 4285 df-if 4461 df-sn 4561 df-pr 4563 df-op 4567 df-opab 5122 df-xp 5554 df-rel 5555 df-isomgr 44060 |
This theorem is referenced by: isisomgr 44063 |
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