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Theorem uhgraopelvv 25826
 Description: An undirected hypergraph is a member in the universal class of ordered pairs. (Contributed by AV, 3-Jan-2020.)
Assertion
Ref Expression
uhgraopelvv (𝐺 ∈ UHGrph → 𝐺 ∈ (V × V))

Proof of Theorem uhgraopelvv
StepHypRef Expression
1 reluhgra 25823 . . . 4 Rel UHGrph
21a1i 11 . . 3 (𝐺 ∈ UHGrph → Rel UHGrph )
3 df-rel 5045 . . 3 (Rel UHGrph ↔ UHGrph ⊆ (V × V))
42, 3sylib 207 . 2 (𝐺 ∈ UHGrph → UHGrph ⊆ (V × V))
5 id 22 . 2 (𝐺 ∈ UHGrph → 𝐺 ∈ UHGrph )
64, 5sseldd 3569 1 (𝐺 ∈ UHGrph → 𝐺 ∈ (V × V))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1977  Vcvv 3173   ⊆ wss 3540   × cxp 5036  Rel wrel 5043   UHGrph cuhg 25819 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-opab 4644  df-xp 5044  df-rel 5045  df-uhgra 25821 This theorem is referenced by:  0eusgraiff0rgracl  26468
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