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Theorem structex 17110
Description: A structure is a set. (Contributed by AV, 10-Nov-2021.)
Assertion
Ref Expression
structex (𝐺 Struct 𝑋𝐺 ∈ V)

Proof of Theorem structex
StepHypRef Expression
1 brstruct 17108 . 2 Rel Struct
21brrelex1i 5728 1 (𝐺 Struct 𝑋𝐺 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2099  Vcvv 3469   class class class wbr 5142   Struct cstr 17106
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698  ax-sep 5293  ax-nul 5300  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-ral 3057  df-rex 3066  df-rab 3428  df-v 3471  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-br 5143  df-opab 5205  df-xp 5678  df-rel 5679  df-struct 17107
This theorem is referenced by:  setsn0fun  17133  setsstruct2  17134  strfv  17164  basprssdmsets  17184  opelstrbas  17185  cnfldexOLD  21284  edgfiedgval  28817  structgrssvtxlem  28823  setsiedg  28836
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