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Mirrors > Home > MPE Home > Th. List > relumgra | Structured version Visualization version GIF version |
Description: The class of all undirected multigraphs is a relation. (Contributed by Mario Carneiro, 11-Mar-2015.) |
Ref | Expression |
---|---|
relumgra | ⊢ Rel UMGrph |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-umgra 25842 | . 2 ⊢ UMGrph = {〈𝑣, 𝑒〉 ∣ 𝑒:dom 𝑒⟶{𝑥 ∈ (𝒫 𝑣 ∖ {∅}) ∣ (#‘𝑥) ≤ 2}} | |
2 | 1 | relopabi 5167 | 1 ⊢ Rel UMGrph |
Colors of variables: wff setvar class |
Syntax hints: {crab 2900 ∖ cdif 3537 ∅c0 3874 𝒫 cpw 4108 {csn 4125 class class class wbr 4583 dom cdm 5038 Rel wrel 5043 ⟶wf 5800 ‘cfv 5804 ≤ cle 9954 2c2 10947 #chash 12979 UMGrph cumg 25841 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-opab 4644 df-xp 5044 df-rel 5045 df-umgra 25842 |
This theorem is referenced by: umgraf2 25846 umgrares 25853 umisuhgra 25856 umgraun 25857 vdgrun 26428 vdgrfiun 26429 iseupa 26492 eupap1 26503 eupath2lem3 26506 eupath2 26507 |
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