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Theorem uvtxssvtx 29275
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 29274 . 2 (𝑛 ∈ (UnivVtx‘𝐺) → 𝑛𝑉)
32ssriv 3980 1 (UnivVtx‘𝐺) ⊆ 𝑉
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wss 3944  cfv 6549  Vtxcvtx 28881  UnivVtxcuvtx 29270
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696  ax-sep 5300  ax-nul 5307  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-ne 2930  df-ral 3051  df-rex 3060  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4323  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4910  df-br 5150  df-opab 5212  df-mpt 5233  df-id 5576  df-xp 5684  df-rel 5685  df-cnv 5686  df-co 5687  df-dm 5688  df-iota 6501  df-fun 6551  df-fv 6557  df-ov 7422  df-uvtx 29271
This theorem is referenced by:  iscplgr  29300  vdiscusgrb  29416
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