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Theorem reldmsets 17199
Description: The structure override operator is a proper operator. (Contributed by Stefan O'Rear, 29-Jan-2015.)
Assertion
Ref Expression
reldmsets Rel dom sSet

Proof of Theorem reldmsets
Dummy variables 𝑒 𝑠 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-sets 17198 . 2 sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒}))
21reldmmpo 7567 1 Rel dom sSet
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3478  cdif 3960  cun 3961  {csn 4631  dom cdm 5689  cres 5691  Rel wrel 5694   sSet csts 17197
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-xp 5695  df-rel 5696  df-dm 5699  df-oprab 7435  df-mpo 7436  df-sets 17198
This theorem is referenced by:  setsnid  17243  setsnidOLD  17244  oduval  18345  oduleval  18346  oppgval  19378  oppgplusfval  19379  mgpval  20155  opprval  20352
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