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Theorem reldmsets 14309
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 14293 . 2  |- sSet  =  ( s  e.  _V , 
e  e.  _V  |->  ( ( s  |`  ( _V  \  dom  { e } ) )  u. 
{ e } ) )
21reldmmpt2 6306 1  |-  Rel  dom sSet
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3072    \ cdif 3428    u. cun 3429   {csn 3980   dom cdm 4943    |` cres 4945   Rel wrel 4948   sSet csts 14285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431  ax-sep 4516  ax-nul 4524  ax-pr 4634
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2265  df-mo 2266  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ne 2647  df-ral 2801  df-rex 2802  df-rab 2805  df-v 3074  df-dif 3434  df-un 3436  df-in 3438  df-ss 3445  df-nul 3741  df-if 3895  df-sn 3981  df-pr 3983  df-op 3987  df-br 4396  df-opab 4454  df-xp 4949  df-rel 4950  df-dm 4953  df-oprab 6199  df-mpt2 6200  df-sets 14293
This theorem is referenced by:  setsnid  14329  oduval  15414  oduleval  15415  oppgval  15976  oppgplusfval  15977  mgpval  16711  opprval  16834
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