Theorem reldmsets 13241

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 13219	. 2 |- sSet = ( s e. _V , e e. _V |-> ( ( s |` ( _V \ dom { e } ) ) u. { e } ) )
2	1	reldmmpo 6165	1 |- Rel dom sSet

Syntax hints:   _Vcvv 2813   \ cdif 3208   u. cun 3209   {csn 3689   dom cdm 4749   |` cres 4751   Rel wrel 4754   sSet csts 13210

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-14 2206  ax-ext 2214  ax-sep 4228  ax-pow 4287  ax-pr 4322

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-eu 2083  df-mo 2084  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-ral 2525  df-rex 2526  df-v 2815  df-un 3215  df-in 3217  df-ss 3224  df-pw 3671  df-sn 3695  df-pr 3696  df-op 3698  df-br 4110  df-opab 4172  df-xp 4755  df-rel 4756  df-dm 4759  df-oprab 6054  df-mpo 6055  df-sets 13219

This theorem is referenced by: (None)