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Mirrors > Home > MPE Home > Th. List > rusgrusgr | Structured version Visualization version GIF version |
Description: A k-regular simple graph is a simple graph. (Contributed by Alexander van der Vekens, 8-Jul-2018.) (Revised by AV, 18-Dec-2020.) |
Ref | Expression |
---|---|
rusgrusgr | ⊢ (𝐺 RegUSGraph 𝐾 → 𝐺 ∈ USGraph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rusgrprop 26458 | . 2 ⊢ (𝐺 RegUSGraph 𝐾 → (𝐺 ∈ USGraph ∧ 𝐺 RegGraph 𝐾)) | |
2 | 1 | simpld 475 | 1 ⊢ (𝐺 RegUSGraph 𝐾 → 𝐺 ∈ USGraph ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1990 class class class wbr 4653 USGraph cusgr 26044 RegGraph crgr 26451 RegUSGraph crusgr 26452 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-rusgr 26454 |
This theorem is referenced by: finrusgrfusgr 26461 rusgr0edg 26868 rusgrnumwwlks 26869 rusgrnumwwlk 26870 rusgrnumwlkg 26872 numclwwlkovf2num 27218 numclwwlk1 27231 |
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