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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 Struct

Proof of Theorem brstruct
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-struct 11998 . 2 Struct
21relopabi 4672 1 Struct
 Colors of variables: wff set class Syntax hints:   w3a 963   wcel 1481   cdif 3072   cin 3074   wss 3075  c0 3367  csn 3531   cxp 4544   cdm 4546   wrel 4551   wfun 5124  cfv 5130   cle 7824  cn 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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