MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  structex Structured version   Visualization version   GIF version

Theorem structex 16482
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 16480 . 2 Rel Struct
21brrelex1i 5601 1 (𝐺 Struct 𝑋𝐺 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  Vcvv 3492   class class class wbr 5057   Struct cstr 16467
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-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-rel 5555  df-struct 16473
This theorem is referenced by:  setsn0fun  16508  setsstruct2  16509  strfv  16519  basprssdmsets  16537  opelstrbas  16585  cnfldex  20476  edgfiedgval  26729  structgrssvtxlem  26735  setsiedg  26748
  Copyright terms: Public domain W3C validator