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Theorem reldmress 12031
Description: The structure restriction is a proper operator, so it can be used with ovprc1 5807. (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 11981 . 2  |-s  =  ( w  e.  _V ,  a  e. 
_V  |->  if ( (
Base `  w )  C_  a ,  w ,  ( w sSet  <. ( Base `  ndx ) ,  ( a  i^i  ( Base `  w ) )
>. ) ) )
21reldmmpo 5882 1  |-  Rel  doms
Colors of variables: wff set class
Syntax hints:   _Vcvv 2686    i^i cin 3070    C_ wss 3071   ifcif 3474   <.cop 3530   dom cdm 4539   Rel wrel 4544   ` cfv 5123  (class class class)co 5774   ndxcnx 11970   sSet csts 11971   Basecbs 11973   ↾s cress 11974
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-rel 4546  df-dm 4549  df-oprab 5778  df-mpo 5779  df-ress 11981
This theorem is referenced by: (None)
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