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Theorem releupa 23880
 Description: The set EulPaths of all Eulerian paths on is a set of pairs by our definition of an Eulerian path, and so is a relation. (Contributed by Mario Carneiro, 12-Mar-2015.)
Assertion
Ref Expression
releupa EulPaths

Proof of Theorem releupa
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-eupa 23864 . 2 EulPaths UMGrph
21relmpt2opab 6201 1 EulPaths
 Colors of variables: wff set class Syntax hints:   wa 358   w3a 934   wceq 1623  wral 2543  wrex 2544  cvv 2788  cpr 3641   class class class wbr 4023   cdm 4689   wrel 4694  wf 5251  wf1o 5254  cfv 5255  (class class class)co 5858  cc0 8737  c1 8738   cmin 9037  cn0 9965  cfz 10782   UMGrph cumg 23860   EulPaths ceup 23861 This theorem is referenced by:  iseupa  23881  eupath  23905 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-iun 3907  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fv 5263  df-ov 5861  df-oprab 5862  df-mpt2 5863  df-1st 6122  df-2nd 6123  df-eupa 23864
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