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Theorem brstruct 11978
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 11971 . 2 Struct = {⟨𝑓, 𝑥⟩ ∣ (𝑥 ∈ ( ≤ ∩ (ℕ × ℕ)) ∧ Fun (𝑓 ∖ {∅}) ∧ dom 𝑓 ⊆ (...‘𝑥))}
21relopabi 4665 1 Rel Struct
Colors of variables: wff set class
Syntax hints:  w3a 962  wcel 1480  cdif 3068  cin 3070  wss 3071  c0 3363  {csn 3527   × cxp 4537  dom cdm 4539  Rel wrel 4544  Fun wfun 5117  cfv 5123  cle 7808  cn 8727  ...cfz 9797   Struct cstr 11965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-opab 3990  df-xp 4545  df-rel 4546  df-struct 11971
This theorem is referenced by:  isstruct2im  11979  structex  11981
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