Theorem reldmress 13145

Description: The structure restriction is a proper operator, so it can be used with ovprc1 6054. (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 13089	. 2 ⊢ ↾s = (𝑦 ∈ V, 𝑥 ∈ V ↦ (𝑦 sSet ⟨(Base‘ndx), (𝑥 ∩ (Base‘𝑦))⟩))
2	1	reldmmpo 6132	1 ⊢ Rel dom ↾s

Syntax hints:  Vcvv 2802   ∩ cin 3199  ⟨cop 3672  dom cdm 4725  Rel wrel 4730  ‘cfv 5326  (class class class)co 6017  ndxcnx 13078   sSet csts 13079  Basecbs 13081   ↾_s cress 13082

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-14 2205  ax-ext 2213  ax-sep 4207  ax-pow 4264  ax-pr 4299

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-eu 2082  df-mo 2083  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-ral 2515  df-rex 2516  df-v 2804  df-un 3204  df-in 3206  df-ss 3213  df-pw 3654  df-sn 3675  df-pr 3676  df-op 3678  df-br 4089  df-opab 4151  df-xp 4731  df-rel 4732  df-dm 4735  df-oprab 6021  df-mpo 6022  df-iress 13089

This theorem is referenced by: (None)