MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  reldmsets Unicode version

Theorem reldmsets 13446
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 13430 . 2  |- sSet  =  ( s  e.  _V , 
e  e.  _V  |->  ( ( s  |`  ( _V  \  dom  { e } ) )  u. 
{ e } ) )
21reldmmpt2 6140 1  |-  Rel  dom sSet
Colors of variables: wff set class
Syntax hints:   _Vcvv 2916    \ cdif 3277    u. cun 3278   {csn 3774   dom cdm 4837    |` cres 4839   Rel wrel 4842   sSet csts 13422
This theorem is referenced by:  setsnid  13464  oduval  14512  oduleval  14513  oppgval  15098  oppgplusfval  15099  mgpval  15606  opprval  15684
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 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363
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 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-br 4173  df-opab 4227  df-xp 4843  df-rel 4844  df-dm 4847  df-oprab 6044  df-mpt2 6045  df-sets 13430
  Copyright terms: Public domain W3C validator