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Theorem reldmsets 12027
 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 12005 . 2 sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒}))
21reldmmpo 5890 1 Rel dom sSet
 Colors of variables: wff set class Syntax hints:  Vcvv 2689   ∖ cdif 3073   ∪ cun 3074  {csn 3532  dom cdm 4547   ↾ cres 4549  Rel wrel 4552   sSet csts 11996 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4054  ax-pow 4106  ax-pr 4139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3080  df-in 3082  df-ss 3089  df-pw 3517  df-sn 3538  df-pr 3539  df-op 3541  df-br 3938  df-opab 3998  df-xp 4553  df-rel 4554  df-dm 4557  df-oprab 5786  df-mpo 5787  df-sets 12005 This theorem is referenced by: (None)
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