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Theorem reldmsets 17045
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 17044 . 2 sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒}))
21reldmmpo 7494 1 Rel dom sSet
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3447  cdif 3911  cun 3912  {csn 4590  dom cdm 5637  cres 5639  Rel wrel 5642   sSet csts 17043
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 5260  ax-nul 5267  ax-pr 5388
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 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-br 5110  df-opab 5172  df-xp 5643  df-rel 5644  df-dm 5647  df-oprab 7365  df-mpo 7366  df-sets 17044
This theorem is referenced by:  setsnid  17089  setsnidOLD  17090  oduval  18185  oduleval  18186  oppgval  19133  oppgplusfval  19134  mgpval  19907  opprval  20058
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