Theorem reldmsets 17076

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.

Step	Hyp	Ref	Expression
1		df-sets 17075	. 2 ⊢ sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒}))
2	1	reldmmpo 7480	1 ⊢ Rel dom sSet

Syntax hints:  Vcvv 3436   ∖ cdif 3894   ∪ cun 3895  {csn 4573  dom cdm 5614   ↾ cres 5616  Rel wrel 5619   sSet csts 17074

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-10 2144  ax-11 2160  ax-12 2180  ax-ext 2703  ax-sep 5232  ax-nul 5242  ax-pr 5368

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2535  df-eu 2564  df-clab 2710  df-cleq 2723  df-clel 2806  df-nfc 2881  df-rab 3396  df-v 3438  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4281  df-if 4473  df-sn 4574  df-pr 4576  df-op 4580  df-br 5090  df-opab 5152  df-xp 5620  df-rel 5621  df-dm 5624  df-oprab 7350  df-mpo 7351  df-sets 17075

This theorem is referenced by:  setsnid  17119  oduval  18194  oduleval  18195  oppgval  19259  oppgplusfval  19260  mgpval  20061  opprval  20256