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Theorem uhgra0 24082
 Description: The empty graph, with vertices but no edges, is a hypergraph, analogous to umgra0 24098. (Contributed by Alexander van der Vekens, 27-Dec-2017.)
Assertion
Ref Expression
uhgra0 UHGrph

Proof of Theorem uhgra0
StepHypRef Expression
1 f0 5766 . . 3
2 dm0 5216 . . . 4
32feq2i 5724 . . 3
41, 3mpbir 209 . 2
5 0ex 4577 . . 3
6 isuhgra 24071 . . 3 UHGrph
75, 6mpan2 671 . 2 UHGrph
84, 7mpbiri 233 1 UHGrph
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wcel 1767  cvv 3113   cdif 3473  c0 3785  cpw 4010  csn 4027   class class class wbr 4447   cdm 4999  wf 5584   UHGrph cuhg 24063 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-pw 4012  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-id 4795  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-fun 5590  df-fn 5591  df-f 5592  df-uhgra 24065 This theorem is referenced by:  uhgra0v  24083
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