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Theorem brstruct 17027
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 17026 . 2 Struct = {⟨𝑓, 𝑥⟩ ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))}
21relopabiv 5781 1 Rel Struct
Colors of variables: wff setvar class
Syntax hints:  w3a 1088  wcel 2107  cdif 3912  cin 3914  wss 3915  c0 4287  {csn 4591   × cxp 5636  dom cdm 5638  Rel wrel 5643  Fun wfun 6495  cfv 6501  cle 11197  cn 12160  ...cfz 13431   Struct cstr 17025
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-in 3922  df-ss 3932  df-opab 5173  df-xp 5644  df-rel 5645  df-struct 17026
This theorem is referenced by:  isstruct2  17028  structex  17029
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