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Theorem usgraedg2 21395
 Description: The value of the "edge function" of a graph is a set containing two elements (the vertices the corresponding edge is connecting), analogous to umgrale 21356. (Contributed by Alexander van der Vekens, 11-Aug-2017.)
Assertion
Ref Expression
usgraedg2 USGrph

Proof of Theorem usgraedg2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 usgraf 21375 . . . 4 USGrph
2 f1f 5639 . . . 4
31, 2syl 16 . . 3 USGrph
43ffvelrnda 5870 . 2 USGrph
5 fveq2 5728 . . . . 5
65eqeq1d 2444 . . . 4
76elrab 3092 . . 3
87simprbi 451 . 2
94, 8syl 16 1 USGrph
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  crab 2709   cdif 3317  c0 3628  cpw 3799  csn 3814   class class class wbr 4212   cdm 4878  wf 5450  wf1 5451  cfv 5454  c2 10049  chash 11618   USGrph cusg 21365 This theorem is referenced by:  usgraedgprv  21396  usgranloopv  21398 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fv 5462  df-usgra 21367
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