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

Theorem structex 17030
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 17028 . 2 Rel Struct
21brrelex1i 5692 1 (𝐺 Struct 𝑋𝐺 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3447   class class class wbr 5109   Struct cstr 17026
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5260  ax-nul 5267  ax-pr 5388
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-br 5110  df-opab 5172  df-xp 5643  df-rel 5644  df-struct 17027
This theorem is referenced by:  setsn0fun  17053  setsstruct2  17054  strfv  17084  basprssdmsets  17104  opelstrbas  17105  cnfldex  20822  edgfiedgval  28017  structgrssvtxlem  28023  setsiedg  28036
  Copyright terms: Public domain W3C validator