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Theorem uhgrfun 26854
Description: The edge function of an undirected hypergraph is a function. (Contributed by Alexander van der Vekens, 26-Dec-2017.) (Revised by AV, 15-Dec-2020.)
Hypothesis
Ref Expression
uhgrfun.e 𝐸 = (iEdg‘𝐺)
Assertion
Ref Expression
uhgrfun (𝐺 ∈ UHGraph → Fun 𝐸)

Proof of Theorem uhgrfun
StepHypRef Expression
1 eqid 2824 . . 3 (Vtx‘𝐺) = (Vtx‘𝐺)
2 uhgrfun.e . . 3 𝐸 = (iEdg‘𝐺)
31, 2uhgrf 26850 . 2 (𝐺 ∈ UHGraph → 𝐸:dom 𝐸⟶(𝒫 (Vtx‘𝐺) ∖ {∅}))
43ffund 6521 1 (𝐺 ∈ UHGraph → Fun 𝐸)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1536  wcel 2113  cdif 3936  c0 4294  𝒫 cpw 4542  {csn 4570  dom cdm 5558  Fun wfun 6352  cfv 6358  Vtxcvtx 26784  iEdgciedg 26785  UHGraphcuhgr 26844
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796  ax-nul 5213
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-mo 2621  df-eu 2653  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-ral 3146  df-rex 3147  df-rab 3150  df-v 3499  df-sbc 3776  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4471  df-pw 4544  df-sn 4571  df-pr 4573  df-op 4577  df-uni 4842  df-br 5070  df-opab 5132  df-rel 5565  df-cnv 5566  df-co 5567  df-dm 5568  df-rn 5569  df-iota 6317  df-fun 6360  df-fn 6361  df-f 6362  df-fv 6366  df-uhgr 26846
This theorem is referenced by:  lpvtx  26856  upgrle2  26893  uhgredgiedgb  26914  uhgriedg0edg0  26915  uhgrvtxedgiedgb  26924  edglnl  26931  numedglnl  26932  uhgr2edg  26993  ushgredgedg  27014  ushgredgedgloop  27016  0uhgrsubgr  27064  uhgrsubgrself  27065  subgruhgrfun  27067  subgruhgredgd  27069  subumgredg2  27070  subupgr  27072  uhgrspansubgrlem  27075  uhgrspansubgr  27076  uhgrspan1  27088  upgrreslem  27089  umgrreslem  27090  upgrres  27091  umgrres  27092  vtxduhgr0e  27263  vtxduhgrun  27268  vtxduhgrfiun  27269  finsumvtxdg2ssteplem1  27330  upgrewlkle2  27391  upgredginwlk  27420  wlkiswwlks1  27648  wlkiswwlksupgr2  27658  umgrwwlks2on  27739  vdn0conngrumgrv2  27978  eulerpathpr  28022  eulercrct  28024  lfuhgr  32368  loop1cycl  32388  umgr2cycllem  32391
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