Theorem reldmress 13010

Description: The structure restriction is a proper operator, so it can be used with ovprc1 6004. (Contributed by Stefan O'Rear, 29-Nov-2014.)

Assertion

Ref	Expression
reldmress	|- Rel dom ↾s

Proof of Theorem reldmress

Dummy variables x y are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-iress 12955	. 2 |- ↾s = ( y e. _V , x e. _V |-> ( y sSet <. ( Base ` ndx ) , ( x i^i ( Base ` y ) ) >. ) )
2	1	reldmmpo 6080	1 |- Rel dom ↾s

Syntax hints:   _Vcvv 2776   i^i cin 3173   <.cop 3646   dom cdm 4693   Rel wrel 4698   ` cfv 5290  (class class class)co 5967   ndxcnx 12944   sSet csts 12945   Basecbs 12947   ↾_s cress 12948

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-iress 12955

This theorem is referenced by: (None)