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Theorem rusgrrgr 27272
Description: A k-regular simple graph is a k-regular graph. (Contributed by Alexander van der Vekens, 8-Jul-2018.) (Revised by AV, 18-Dec-2020.)
Assertion
Ref Expression
rusgrrgr (𝐺 RegUSGraph 𝐾𝐺 RegGraph 𝐾)

Proof of Theorem rusgrrgr
StepHypRef Expression
1 rusgrprop 27271 . 2 (𝐺 RegUSGraph 𝐾 → (𝐺 ∈ USGraph ∧ 𝐺 RegGraph 𝐾))
21simprd 496 1 (𝐺 RegUSGraph 𝐾𝐺 RegGraph 𝐾)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105   class class class wbr 5057  USGraphcusgr 26861   RegGraph crgr 27264   RegUSGraph crusgr 27265
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790  ax-sep 5194  ax-nul 5201  ax-pr 5320
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-mo 2615  df-eu 2647  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-rex 3141  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-br 5058  df-opab 5120  df-xp 5554  df-rusgr 27267
This theorem is referenced by:  0grrgr  27289  rgrprc  27300  frrusgrord  28047
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