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Theorem reldmsets 13418
Description: The structure override operator is a proper operator. (Contributed by Stefan O'Rear, 29-Jan-2015.)
Assertion
Ref Expression
reldmsets  |-  Rel  dom sSet

Proof of Theorem reldmsets
Dummy variables  e 
s are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-sets 13402 . 2  |- sSet  =  ( s  e.  _V , 
e  e.  _V  |->  ( ( s  |`  ( _V  \  dom  { e } ) )  u. 
{ e } ) )
21reldmmpt2 6120 1  |-  Rel  dom sSet
Colors of variables: wff set class
Syntax hints:   _Vcvv 2899    \ cdif 3260    u. cun 3261   {csn 3757   dom cdm 4818    |` cres 4820   Rel wrel 4823   sSet csts 13394
This theorem is referenced by:  setsnid  13436  oduval  14484  oduleval  14485  oppgval  15070  oppgplusfval  15071  mgpval  15578  opprval  15656
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2242  df-mo 2243  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-br 4154  df-opab 4208  df-xp 4824  df-rel 4825  df-dm 4828  df-oprab 6024  df-mpt2 6025  df-sets 13402
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