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Theorem rusgrrgr 26693
 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 (𝐺RegUSGraph𝐾𝐺RegGraph𝐾)

Proof of Theorem rusgrrgr
StepHypRef Expression
1 rusgrprop 26692 . 2 (𝐺RegUSGraph𝐾 → (𝐺 ∈ USGraph ∧ 𝐺RegGraph𝐾))
21simprd 477 1 (𝐺RegUSGraph𝐾𝐺RegGraph𝐾)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2144   class class class wbr 4784  USGraphcusgr 26265  RegGraphcrgr 26685  RegUSGraphcrusgr 26686 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-nul 4920  ax-pr 5034 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-eu 2621  df-mo 2622  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ne 2943  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-br 4785  df-opab 4845  df-rusgr 26688 This theorem is referenced by:  0grrgr  26710  rgrprc  26721  frrusgrord  27520
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