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Theorem uvtxssvtx 27224
 Description: The set of the universal vertices is a subset of the set of all vertices. (Contributed by AV, 23-Dec-2020.)
Hypothesis
Ref Expression
uvtxel.v 𝑉 = (Vtx‘𝐺)
Assertion
Ref Expression
uvtxssvtx (UnivVtx‘𝐺) ⊆ 𝑉

Proof of Theorem uvtxssvtx
Dummy variable 𝑛 is distinct from all other variables.
StepHypRef Expression
1 uvtxel.v . . 3 𝑉 = (Vtx‘𝐺)
21uvtxisvtx 27223 . 2 (𝑛 ∈ (UnivVtx‘𝐺) → 𝑛𝑉)
32ssriv 3921 1 (UnivVtx‘𝐺) ⊆ 𝑉
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ⊆ wss 3883  ‘cfv 6332  Vtxcvtx 26833  UnivVtxcuvtx 27219 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5171  ax-nul 5178  ax-pr 5299 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ne 2988  df-ral 3111  df-rex 3112  df-rab 3115  df-v 3444  df-sbc 3723  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4805  df-br 5035  df-opab 5097  df-mpt 5115  df-id 5429  df-xp 5529  df-rel 5530  df-cnv 5531  df-co 5532  df-dm 5533  df-iota 6291  df-fun 6334  df-fv 6340  df-ov 7148  df-uvtx 27220 This theorem is referenced by:  iscplgr  27249  vdiscusgrb  27364
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