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Theorem brstruct 12005
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 11998 . 2  |- Struct  =  { <. f ,  x >.  |  ( x  e.  (  <_  i^i  ( NN  X.  NN ) )  /\  Fun  ( f  \  { (/)
} )  /\  dom  f  C_  ( ... `  x
) ) }
21relopabi 4672 1  |-  Rel Struct
Colors of variables: wff set class
Syntax hints:    /\ w3a 963    e. wcel 1481    \ cdif 3072    i^i cin 3074    C_ wss 3075   (/)c0 3367   {csn 3531    X. cxp 4544   dom cdm 4546   Rel wrel 4551   Fun wfun 5124   ` cfv 5130    <_ cle 7824   NNcn 8743   ...cfz 9820   Struct cstr 11992
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4053  ax-pow 4105  ax-pr 4138
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-pw 3516  df-sn 3537  df-pr 3538  df-op 3540  df-opab 3997  df-xp 4552  df-rel 4553  df-struct 11998
This theorem is referenced by:  isstruct2im  12006  structex  12008
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