Theorem reldmress 13394

Description: The structure restriction is a proper operator, so it can be used with ovprc1 6112. (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 13338	. 2 ⊢ ↾s = (𝑦 ∈ V, 𝑥 ∈ V ↦ (𝑦 sSet ⟨(Base‘ndx), (𝑥 ∩ (Base‘𝑦))⟩))
2	1	reldmmpo 6190	1 ⊢ Rel dom ↾s

Syntax hints:  Vcvv 2821   ∩ cin 3219  ⟨cop 3708  dom cdm 4769  Rel wrel 4774  ‘cfv 5372  (class class class)co 6075  ndxcnx 13327   sSet csts 13328  Basecbs 13330   ↾_s cress 13331

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-14 2212  ax-ext 2220  ax-sep 4244  ax-pow 4306  ax-pr 4341

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-eu 2089  df-mo 2090  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ral 2533  df-rex 2534  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-pw 3687  df-sn 3711  df-pr 3712  df-op 3714  df-br 4126  df-opab 4188  df-xp 4775  df-rel 4776  df-dm 4779  df-oprab 6079  df-mpo 6080  df-iress 13338

This theorem is referenced by: (None)