Theorem reldmress 12895

Description: The structure restriction is a proper operator, so it can be used with ovprc1 5981. (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 12840	. 2 |- ↾s = ( y e. _V , x e. _V |-> ( y sSet <. ( Base ` ndx ) , ( x i^i ( Base ` y ) ) >. ) )
2	1	reldmmpo 6057	1 |- Rel dom ↾s

Syntax hints:   _Vcvv 2772   i^i cin 3165   <.cop 3636   dom cdm 4675   Rel wrel 4680   ` cfv 5271  (class class class)co 5944   ndxcnx 12829   sSet csts 12830   Basecbs 12832   ↾_s cress 12833

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-14 2179  ax-ext 2187  ax-sep 4162  ax-pow 4218  ax-pr 4253

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-eu 2057  df-mo 2058  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-ral 2489  df-rex 2490  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-pw 3618  df-sn 3639  df-pr 3640  df-op 3642  df-br 4045  df-opab 4106  df-xp 4681  df-rel 4682  df-dm 4685  df-oprab 5948  df-mpo 5949  df-iress 12840

This theorem is referenced by: (None)