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Theorem reldmress 15842
Description: The structure restriction is a proper operator, so it can be used with ovprc1 6638. (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 15783 . 2 s = (𝑤 ∈ V, 𝑎 ∈ V ↦ if((Base‘𝑤) ⊆ 𝑎, 𝑤, (𝑤 sSet ⟨(Base‘ndx), (𝑎 ∩ (Base‘𝑤))⟩)))
21reldmmpt2 6725 1 Rel dom ↾s
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3191  cin 3559  wss 3560  ifcif 4063  cop 4159  dom cdm 5079  Rel wrel 5084  cfv 5850  (class class class)co 6605  ndxcnx 15773   sSet csts 15774  Basecbs 15776  s cress 15777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606  ax-sep 4746  ax-nul 4754  ax-pr 4872
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-eu 2478  df-mo 2479  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756  df-rab 2921  df-v 3193  df-dif 3563  df-un 3565  df-in 3567  df-ss 3574  df-nul 3897  df-if 4064  df-sn 4154  df-pr 4156  df-op 4160  df-br 4619  df-opab 4679  df-xp 5085  df-rel 5086  df-dm 5089  df-oprab 6609  df-mpt2 6610  df-ress 15783
This theorem is referenced by:  ressbas  15846  ressbasss  15848  resslem  15849  ress0  15850  ressinbas  15852  ressress  15854  wunress  15856  subcmn  18158  srasca  19095  rlmsca2  19115  resstopn  20895  cphsubrglem  22880  submomnd  29487  suborng  29592
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