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

Theorem structex 17082
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 17080 . 2 Rel Struct
21brrelex1i 5732 1 (𝐺 Struct 𝑋𝐺 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Vcvv 3474   class class class wbr 5148   Struct cstr 17078
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-sep 5299  ax-nul 5306  ax-pr 5427
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-xp 5682  df-rel 5683  df-struct 17079
This theorem is referenced by:  setsn0fun  17105  setsstruct2  17106  strfv  17136  basprssdmsets  17156  opelstrbas  17157  cnfldex  20946  edgfiedgval  28274  structgrssvtxlem  28280  setsiedg  28293
  Copyright terms: Public domain W3C validator