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Theorem reldmsets 14742
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 14725 . 2  |- sSet  =  ( s  e.  _V , 
e  e.  _V  |->  ( ( s  |`  ( _V  \  dom  { e } ) )  u. 
{ e } ) )
21reldmmpt2 6386 1  |-  Rel  dom sSet
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3106    \ cdif 3458    u. cun 3459   {csn 4016   dom cdm 4988    |` cres 4990   Rel wrel 4993   sSet csts 14717
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-9 1827  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-sep 4560  ax-nul 4568  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-eu 2288  df-mo 2289  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-br 4440  df-opab 4498  df-xp 4994  df-rel 4995  df-dm 4998  df-oprab 6274  df-mpt2 6275  df-sets 14725
This theorem is referenced by:  setsnid  14763  oduval  15962  oduleval  15963  oppgval  16584  oppgplusfval  16585  mgpval  17342  opprval  17471
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