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Theorem brstruct 16492
 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 16485 . 2 Struct = {⟨𝑓, 𝑥⟩ ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))}
21relopabi 5681 1 Rel Struct
 Colors of variables: wff setvar class Syntax hints:   ∧ w3a 1084   ∈ wcel 2115   ∖ cdif 3916   ∩ cin 3918   ⊆ wss 3919  ∅c0 4276  {csn 4550   × cxp 5540  dom cdm 5542  Rel wrel 5547  Fun wfun 6337  ‘cfv 6343   ≤ cle 10674  ℕcn 11634  ...cfz 12894   Struct cstr 16479 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 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-opab 5115  df-xp 5548  df-rel 5549  df-struct 16485 This theorem is referenced by:  isstruct2  16493  structex  16494
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