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Theorem brstruct 13479
 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 13473 . 2 Struct
21relopabi 5002 1 Struct
 Colors of variables: wff set class Syntax hints:   w3a 937   wcel 1726   cdif 3319   cin 3321   wss 3322  c0 3630  csn 3816   cxp 4878   cdm 4880   wrel 4885   wfun 5450  cfv 5456   cle 9123  cn 10002  cfz 11045   Struct cstr 13467 This theorem is referenced by:  isstruct2  13480  strfv  13503  cnfldex  16708 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269  df-xp 4886  df-rel 4887  df-struct 13473
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