Theorem reldmress 13096

Description: The structure restriction is a proper operator, so it can be used with ovprc1 6038. (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 13040	. 2 |- ↾s = ( y e. _V , x e. _V |-> ( y sSet <. ( Base ` ndx ) , ( x i^i ( Base ` y ) ) >. ) )
2	1	reldmmpo 6116	1 |- Rel dom ↾s

Syntax hints:   _Vcvv 2799   i^i cin 3196   <.cop 3669   dom cdm 4719   Rel wrel 4724   ` cfv 5318  (class class class)co 6001   ndxcnx 13029   sSet csts 13030   Basecbs 13032   ↾_s cress 13033

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-14 2203  ax-ext 2211  ax-sep 4202  ax-pow 4258  ax-pr 4293

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-pw 3651  df-sn 3672  df-pr 3673  df-op 3675  df-br 4084  df-opab 4146  df-xp 4725  df-rel 4726  df-dm 4729  df-oprab 6005  df-mpo 6006  df-iress 13040

This theorem is referenced by: (None)