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Theorem releupa 21686
 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 21685 . 2 EulPaths UMGrph
21relmpt2opab 6429 1 EulPaths
 Colors of variables: wff set class Syntax hints:   wa 359   w3a 936   wceq 1652  wral 2705  wrex 2706  cvv 2956  cpr 3815   class class class wbr 4212   cdm 4878   wrel 4883  wf 5450  wf1o 5453  cfv 5454  (class class class)co 6081  cc0 8990  c1 8991   cmin 9291  cn0 10221  cfz 11043   UMGrph cumg 21347   EulPaths ceup 21684 This theorem is referenced by:  eupath  21703 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350  df-eupa 21685
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