Theorem reldmress 13360

Description: The structure restriction is a proper operator, so it can be used with ovprc1 6095. (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 13304	. 2 |- ↾s = ( y e. _V , x e. _V |-> ( y sSet <. ( Base ` ndx ) , ( x i^i ( Base ` y ) ) >. ) )
2	1	reldmmpo 6173	1 |- Rel dom ↾s

Syntax hints:   _Vcvv 2815   i^i cin 3213   <.cop 3697   dom cdm 4754   Rel wrel 4759   ` cfv 5357  (class class class)co 6058   ndxcnx 13293   sSet csts 13294   Basecbs 13296   ↾_s cress 13297

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 2208  ax-ext 2216  ax-sep 4233  ax-pow 4292  ax-pr 4327

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-eu 2085  df-mo 2086  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-ral 2527  df-rex 2528  df-v 2817  df-un 3218  df-in 3220  df-ss 3227  df-pw 3676  df-sn 3700  df-pr 3701  df-op 3703  df-br 4115  df-opab 4177  df-xp 4760  df-rel 4761  df-dm 4764  df-oprab 6062  df-mpo 6063  df-iress 13304

This theorem is referenced by: (None)