Theorem structex 17120

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 17118	. 2 ⊢ Rel Struct
2	1	brrelex1i 5687	1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2114  Vcvv 3429   class class class wbr 5085   Struct cstr 17116

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 2708  ax-sep 5231  ax-pr 5375

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 2715  df-cleq 2728  df-clel 2811  df-ral 3052  df-rex 3062  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-in 3896  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-br 5086  df-opab 5148  df-xp 5637  df-rel 5638  df-struct 17117

This theorem is referenced by:  setsn0fun  17143  setsstruct2  17144  strfv  17173  basprssdmsets  17191  opelstrbas  17192  edgfiedgval  29086  structgrssvtxlem  29092  setsiedg  29105