Theorem reldmress 12980

Description: The structure restriction is a proper operator, so it can be used with ovprc1 5999. (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 12925	. 2 ⊢ ↾s = (𝑦 ∈ V, 𝑥 ∈ V ↦ (𝑦 sSet ⟨(Base‘ndx), (𝑥 ∩ (Base‘𝑦))⟩))
2	1	reldmmpo 6075	1 ⊢ Rel dom ↾s

Syntax hints:  Vcvv 2773   ∩ cin 3169  ⟨cop 3641  dom cdm 4688  Rel wrel 4693  ‘cfv 5285  (class class class)co 5962  ndxcnx 12914   sSet csts 12915  Basecbs 12917   ↾_s cress 12918

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-14 2180  ax-ext 2188  ax-sep 4173  ax-pow 4229  ax-pr 4264

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-ral 2490  df-rex 2491  df-v 2775  df-un 3174  df-in 3176  df-ss 3183  df-pw 3623  df-sn 3644  df-pr 3645  df-op 3647  df-br 4055  df-opab 4117  df-xp 4694  df-rel 4695  df-dm 4698  df-oprab 5966  df-mpo 5967  df-iress 12925

This theorem is referenced by: (None)