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Theorem brstruct 16777
Description: The structure relation is a relation. (Contributed by Mario Carneiro, 29-Aug-2015.)
Assertion
Ref Expression
brstruct Rel Struct

Proof of Theorem brstruct
Dummy variables 𝑥 𝑓 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-struct 16776 . 2 Struct = {⟨𝑓, 𝑥⟩ ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))}
21relopabiv 5719 1 Rel Struct
Colors of variables: wff setvar class
Syntax hints:  w3a 1085  wcel 2108  cdif 3880  cin 3882  wss 3883  c0 4253  {csn 4558   × cxp 5578  dom cdm 5580  Rel wrel 5585  Fun wfun 6412  cfv 6418  cle 10941  cn 11903  ...cfz 13168   Struct cstr 16775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-opab 5133  df-xp 5586  df-rel 5587  df-struct 16776
This theorem is referenced by:  isstruct2  16778  structex  16779
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