Theorem reldmsets 12976

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 12954	. 2 |- sSet = ( s e. _V , e e. _V |-> ( ( s |` ( _V \ dom { e } ) ) u. { e } ) )
2	1	reldmmpo 6080	1 |- Rel dom sSet

Syntax hints:   _Vcvv 2776   \ cdif 3171   u. cun 3172   {csn 3643   dom cdm 4693   |` cres 4695   Rel wrel 4698   sSet csts 12945

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-14 2181  ax-ext 2189  ax-sep 4178  ax-pow 4234  ax-pr 4269

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-ral 2491  df-rex 2492  df-v 2778  df-un 3178  df-in 3180  df-ss 3187  df-pw 3628  df-sn 3649  df-pr 3650  df-op 3652  df-br 4060  df-opab 4122  df-xp 4699  df-rel 4700  df-dm 4703  df-oprab 5971  df-mpo 5972  df-sets 12954

This theorem is referenced by: (None)