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Theorem brstruct 11750
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 11743 . 2  |- Struct  =  { <. f ,  x >.  |  ( x  e.  (  <_  i^i  ( NN  X.  NN ) )  /\  Fun  ( f  \  { (/)
} )  /\  dom  f  C_  ( ... `  x
) ) }
21relopabi 4603 1  |-  Rel Struct
Colors of variables: wff set class
Syntax hints:    /\ w3a 930    e. wcel 1448    \ cdif 3018    i^i cin 3020    C_ wss 3021   (/)c0 3310   {csn 3474    X. cxp 4475   dom cdm 4477   Rel wrel 4482   Fun wfun 5053   ` cfv 5059    <_ cle 7673   NNcn 8578   ...cfz 9631   Struct cstr 11737
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-14 1460  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986  ax-pow 4038  ax-pr 4069
This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-rex 2381  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-pw 3459  df-sn 3480  df-pr 3481  df-op 3483  df-opab 3930  df-xp 4483  df-rel 4484  df-struct 11743
This theorem is referenced by:  isstruct2im  11751  structex  11753
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