Theorem structex 17081

Description: A structure is a set. (Contributed by AV, 10-Nov-2021.)

Assertion

Ref	Expression
structex	⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V)

Proof of Theorem structex

Step	Hyp	Ref	Expression
1		brstruct 17079	. 2 ⊢ Rel Struct
2	1	brrelex1i 5681	1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2114  Vcvv 3441   class class class wbr 5099   Struct cstr 17077

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5242  ax-nul 5252  ax-pr 5378

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ral 3053  df-rex 3062  df-rab 3401  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-if 4481  df-sn 4582  df-pr 4584  df-op 4588  df-br 5100  df-opab 5162  df-xp 5631  df-rel 5632  df-struct 17078

This theorem is referenced by:  setsn0fun  17104  setsstruct2  17105  strfv  17134  basprssdmsets  17152  opelstrbas  17153  cnfldexOLD  21331  edgfiedgval  29094  structgrssvtxlem  29100  setsiedg  29113