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Theorem residOLD 5616
 Description: Obsolete as of 19-Feb-2022. Use dfrel3 5748 instead. (Contributed by NM, 16-Mar-2004.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
residOLD (Rel 𝐴 → (𝐴 ↾ V) = 𝐴)

Proof of Theorem residOLD
StepHypRef Expression
1 ssv 3764 . 2 dom 𝐴 ⊆ V
2 relssres 5593 . 2 ((Rel 𝐴 ∧ dom 𝐴 ⊆ V) → (𝐴 ↾ V) = 𝐴)
31, 2mpan2 709 1 (Rel 𝐴 → (𝐴 ↾ V) = 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1630  Vcvv 3338   ⊆ wss 3713  dom cdm 5264   ↾ cres 5266  Rel wrel 5269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-9 2146  ax-10 2166  ax-11 2181  ax-12 2194  ax-13 2389  ax-ext 2738  ax-sep 4931  ax-nul 4939  ax-pr 5053 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2045  df-clab 2745  df-cleq 2751  df-clel 2754  df-nfc 2889  df-ral 3053  df-rex 3054  df-rab 3057  df-v 3340  df-dif 3716  df-un 3718  df-in 3720  df-ss 3727  df-nul 4057  df-if 4229  df-sn 4320  df-pr 4322  df-op 4326  df-br 4803  df-opab 4863  df-xp 5270  df-rel 5271  df-dm 5274  df-res 5276 This theorem is referenced by: (None)
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