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Theorem reldmress 17276
Description: The structure restriction is a proper operator, so it can be used with ovprc1 7470. (Contributed by Stefan O'Rear, 29-Nov-2014.)
Assertion
Ref Expression
reldmress Rel dom ↾s

Proof of Theorem reldmress
Dummy variables 𝑤 𝑎 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ress 17275 . 2 s = (𝑤 ∈ V, 𝑎 ∈ V ↦ if((Base‘𝑤) ⊆ 𝑎, 𝑤, (𝑤 sSet ⟨(Base‘ndx), (𝑎 ∩ (Base‘𝑤))⟩)))
21reldmmpo 7567 1 Rel dom ↾s
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3480  cin 3950  wss 3951  ifcif 4525  cop 4632  dom cdm 5685  Rel wrel 5690  cfv 6561  (class class class)co 7431   sSet csts 17200  ndxcnx 17230  Basecbs 17247  s cress 17274
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-opab 5206  df-xp 5691  df-rel 5692  df-dm 5695  df-oprab 7435  df-mpo 7436  df-ress 17275
This theorem is referenced by:  ressbas  17280  ressbasOLD  17281  ressbasssg  17282  ressbasssOLD  17285  resseqnbas  17287  resslemOLD  17288  ress0  17289  ressinbas  17291  ressress  17293  wunress  17295  wunressOLD  17296  subcmn  19855  srasca  21183  srascaOLD  21184  rlmsca2  21206  resstopn  23194  cphsubrglem  25211  submomnd  33087  suborng  33345
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