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Theorem eupthiswlk 30066
Description: An Eulerian path is a walk. (Contributed by AV, 6-Apr-2021.)
Assertion
Ref Expression
eupthiswlk (𝐹(EulerPaths‘𝐺)𝑃𝐹(Walks‘𝐺)𝑃)

Proof of Theorem eupthiswlk
StepHypRef Expression
1 eupthistrl 30065 . 2 (𝐹(EulerPaths‘𝐺)𝑃𝐹(Trails‘𝐺)𝑃)
2 trliswlk 29555 . 2 (𝐹(Trails‘𝐺)𝑃𝐹(Walks‘𝐺)𝑃)
31, 2syl 17 1 (𝐹(EulerPaths‘𝐺)𝑃𝐹(Walks‘𝐺)𝑃)
Colors of variables: wff setvar class
Syntax hints:  wi 4   class class class wbr 5143  cfv 6543  Walkscwlks 29454  Trailsctrls 29548  EulerPathsceupth 30051
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696  ax-sep 5294  ax-nul 5301  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-ne 2931  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3465  df-sbc 3769  df-csb 3885  df-dif 3942  df-un 3944  df-in 3946  df-ss 3956  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4904  df-br 5144  df-opab 5206  df-mpt 5227  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-res 5684  df-ima 5685  df-iota 6495  df-fun 6545  df-fn 6546  df-fo 6549  df-fv 6551  df-ov 7419  df-wlks 29457  df-trls 29550  df-eupth 30052
This theorem is referenced by:  eupthpf  30067  eupthp1  30070  eupth2eucrct  30071  eupth2lem3  30090  eupth2lems  30092  eupth2  30093  eucrct2eupth1  30098
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