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Theorem reldmress 12502
Description: The structure restriction is a proper operator, so it can be used with ovprc1 5905. (Contributed by Stefan O'Rear, 29-Nov-2014.)
Assertion
Ref Expression
reldmress  |-  Rel  doms

Proof of Theorem reldmress
Dummy variables  x  y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-iress 12450 . 2  |-s  =  ( y  e.  _V ,  x  e. 
_V  |->  ( y sSet  <. (
Base `  ndx ) ,  ( x  i^i  ( Base `  y ) )
>. ) )
21reldmmpo 5980 1  |-  Rel  doms
Colors of variables: wff set class
Syntax hints:   _Vcvv 2737    i^i cin 3128   <.cop 3594   dom cdm 4623   Rel wrel 4628   ` cfv 5212  (class class class)co 5869   ndxcnx 12439   sSet csts 12440   Basecbs 12442   ↾s cress 12443
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-14 2151  ax-ext 2159  ax-sep 4118  ax-pow 4171  ax-pr 4206
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-pw 3576  df-sn 3597  df-pr 3598  df-op 3600  df-br 4001  df-opab 4062  df-xp 4629  df-rel 4630  df-dm 4633  df-oprab 5873  df-mpo 5874  df-iress 12450
This theorem is referenced by: (None)
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