Theorem reldmsets 17126

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 17125	. 2 ⊢ sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒}))
2	1	reldmmpo 7490	1 ⊢ Rel dom sSet

Syntax hints:  Vcvv 3431   ∖ cdif 3880   ∪ cun 3881  {csn 4555  dom cdm 5618   ↾ cres 5620  Rel wrel 5623   sSet csts 17124

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-10 2152  ax-11 2168  ax-12 2189  ax-ext 2711  ax-sep 5218  ax-pr 5362

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-nf 1791  df-sb 2074  df-mo 2543  df-eu 2573  df-clab 2718  df-cleq 2731  df-clel 2814  df-nfc 2888  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4262  df-if 4455  df-sn 4556  df-pr 4558  df-op 4562  df-br 5073  df-opab 5135  df-xp 5624  df-rel 5625  df-dm 5628  df-oprab 7360  df-mpo 7361  df-sets 17125

This theorem is referenced by:  setsnid  17169  oduval  18245  oduleval  18246  oppgval  19313  oppgplusfval  19314  mgpval  20115  opprval  20309