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Theorem reldmress 17119
Description: The structure restriction is a proper operator, so it can be used with ovprc1 7397. (Contributed by Stefan O'Rear, 29-Nov-2014.)
Assertion
Ref Expression
reldmress Rel dom β†Ύs

Proof of Theorem reldmress
Dummy variables 𝑀 π‘Ž are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ress 17118 . 2 β†Ύs = (𝑀 ∈ V, π‘Ž ∈ V ↦ if((Baseβ€˜π‘€) βŠ† π‘Ž, 𝑀, (𝑀 sSet ⟨(Baseβ€˜ndx), (π‘Ž ∩ (Baseβ€˜π‘€))⟩)))
21reldmmpo 7491 1 Rel dom β†Ύs
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3444   ∩ cin 3910   βŠ† wss 3911  ifcif 4487  βŸ¨cop 4593  dom cdm 5634  Rel wrel 5639  β€˜cfv 6497  (class class class)co 7358   sSet csts 17040  ndxcnx 17070  Basecbs 17088   β†Ύs cress 17117
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-xp 5640  df-rel 5641  df-dm 5644  df-oprab 7362  df-mpo 7363  df-ress 17118
This theorem is referenced by:  ressbas  17123  ressbasOLD  17124  ressbasss  17126  resseqnbas  17127  resslemOLD  17128  ress0  17129  ressinbas  17131  ressress  17134  wunress  17136  wunressOLD  17137  subcmn  19620  srasca  20662  srascaOLD  20663  rlmsca2  20686  resstopn  22553  cphsubrglem  24557  submomnd  31967  suborng  32157  ressbasssg  40714
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