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

Theorem structex 17192
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 17190 . 2 Rel Struct
21brrelex1i 5755 1 (𝐺 Struct 𝑋𝐺 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2103  Vcvv 3482   class class class wbr 5169   Struct cstr 17188
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-ext 2705  ax-sep 5320  ax-nul 5327  ax-pr 5450
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3064  df-rex 3073  df-rab 3439  df-v 3484  df-dif 3973  df-un 3975  df-ss 3987  df-nul 4348  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-br 5170  df-opab 5232  df-xp 5705  df-rel 5706  df-struct 17189
This theorem is referenced by:  setsn0fun  17215  setsstruct2  17216  strfv  17246  basprssdmsets  17266  opelstrbas  17267  cnfldexOLD  21400  edgfiedgval  29043  structgrssvtxlem  29049  setsiedg  29062
  Copyright terms: Public domain W3C validator