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Theorem reldmress 13517
Description: The structure restriction is a proper operator, so it can be used with ovprc1 6111. (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 13478 . 2  |-s  =  ( w  e.  _V ,  a  e. 
_V  |->  if ( (
Base `  w )  C_  a ,  w ,  ( w sSet  <. ( Base `  ndx ) ,  ( a  i^i  ( Base `  w ) )
>. ) ) )
21reldmmpt2 6183 1  |-  Rel  doms
Colors of variables: wff set class
Syntax hints:   _Vcvv 2958    i^i cin 3321    C_ wss 3322   ifcif 3741   <.cop 3819   dom cdm 4880   Rel wrel 4885   ` cfv 5456  (class class class)co 6083   ndxcnx 13468   sSet csts 13469   Basecbs 13471   ↾s cress 13472
This theorem is referenced by:  ressbas  13521  ressbasss  13523  resslem  13524  ress0  13525  ressinbas  13527  ressress  13528  wunress  13530  subcmn  15458  srasca  16255  rlmsca2  16274  resstopn  17252  cphsubrglem  19142  subofld  24247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-xp 4886  df-rel 4887  df-dm 4890  df-oprab 6087  df-mpt2 6088  df-ress 13478
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