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Theorem brstruct 17197
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 17196 . 2 Struct = {⟨𝑓, 𝑥⟩ ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))}
21relopabiv 5844 1 Rel Struct
Colors of variables: wff setvar class
Syntax hints:  w3a 1087  wcel 2108  cdif 3973  cin 3975  wss 3976  c0 4352  {csn 4648   × cxp 5698  dom cdm 5700  Rel wrel 5705  Fun wfun 6569  cfv 6575  cle 11327  cn 12295  ...cfz 13569   Struct cstr 17195
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 2110  ax-9 2118  ax-ext 2711
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-ss 3993  df-opab 5229  df-xp 5706  df-rel 5707  df-struct 17196
This theorem is referenced by:  isstruct2  17198  structex  17199
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