Theorem structex 17115

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 17113	. 2 ⊢ Rel Struct
2	1	brrelex1i 5682	1 ⊢ (𝐺 Struct 𝑋 → 𝐺 ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2114  Vcvv 3430   class class class wbr 5086   Struct cstr 17111

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 5232  ax-pr 5372

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 3063  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-br 5087  df-opab 5149  df-xp 5632  df-rel 5633  df-struct 17112

This theorem is referenced by:  setsn0fun  17138  setsstruct2  17139  strfv  17168  basprssdmsets  17186  opelstrbas  17187  cnfldexOLD  21366  edgfiedgval  29104  structgrssvtxlem  29110  setsiedg  29123