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Theorem usgraedg2 24037
 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 23984. (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 24009 . . . 4 USGrph
2 f1f 5772 . . . 4
31, 2syl 16 . . 3 USGrph
43ffvelrnda 6012 . 2 USGrph
5 fveq2 5857 . . . . 5
65eqeq1d 2462 . . . 4
76elrab 3254 . . 3
87simprbi 464 . 2
94, 8syl 16 1 USGrph
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1374   wcel 1762  crab 2811   cdif 3466  c0 3778  cpw 4003  csn 4020   class class class wbr 4440   cdm 4992  wf 5575  wf1 5576  cfv 5579  c2 10574  chash 12360   USGrph cusg 23993 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-sep 4561  ax-nul 4569  ax-pr 4679 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-mo 2273  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3108  df-sbc 3325  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-pw 4005  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-br 4441  df-opab 4499  df-id 4788  df-xp 4998  df-rel 4999  df-cnv 5000  df-co 5001  df-dm 5002  df-rn 5003  df-iota 5542  df-fun 5581  df-fn 5582  df-f 5583  df-f1 5584  df-fv 5587  df-usgra 23996 This theorem is referenced by:  usgraedgprv  24038  usgranloopv  24040
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