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Theorem reldmress 13210
Description: The structure restriction is a proper operator, so it can be used with ovprc1 5902. (Contributed by Stefan O'Rear, 29-Nov-2014.)
Assertion
Ref Expression
reldmress  |-  Rel  doms

Proof of Theorem reldmress
Dummy variables  w  a are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ress 13171 . 2  |-s  =  ( w  e.  _V ,  a  e. 
_V  |->  if ( (
Base `  w )  C_  a ,  w ,  ( w sSet  <. ( Base `  ndx ) ,  ( a  i^i  ( Base `  w ) )
>. ) ) )
21reldmmpt2 5971 1  |-  Rel  doms
Colors of variables: wff set class
Syntax hints:   _Vcvv 2801    i^i cin 3164    C_ wss 3165   ifcif 3578   <.cop 3656   dom cdm 4705   Rel wrel 4710   ` cfv 5271  (class class class)co 5874   ndxcnx 13161   sSet csts 13162   Basecbs 13164   ↾s cress 13165
This theorem is referenced by:  ressbas  13214  ressbasss  13216  resslem  13217  ress0  13218  ressinbas  13220  ressress  13221  wunress  13223  subcmn  15149  srasca  15950  rlmsca2  15969  resstopn  16932  cphsubrglem  18629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-xp 4711  df-rel 4712  df-dm 4715  df-oprab 5878  df-mpt2 5879  df-ress 13171
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