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Theorem dfrel3 6061
Description: Alternate definition of relation. (Contributed by NM, 14-May-2008.)
Assertion
Ref Expression
dfrel3 (Rel 𝑅 ↔ (𝑅 ↾ V) = 𝑅)

Proof of Theorem dfrel3
StepHypRef Expression
1 dfrel2 6052 . 2 (Rel 𝑅𝑅 = 𝑅)
2 cnvcnv2 6056 . . 3 𝑅 = (𝑅 ↾ V)
32eqeq1i 2742 . 2 (𝑅 = 𝑅 ↔ (𝑅 ↾ V) = 𝑅)
41, 3bitri 278 1 (Rel 𝑅 ↔ (𝑅 ↾ V) = 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wb 209   = wceq 1543  Vcvv 3408  ccnv 5550  cres 5553  Rel wrel 5556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-12 2175  ax-ext 2708  ax-sep 5192  ax-nul 5199  ax-pr 5322
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3070  df-v 3410  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-if 4440  df-sn 4542  df-pr 4544  df-op 4548  df-br 5054  df-opab 5116  df-xp 5557  df-rel 5558  df-cnv 5559  df-res 5563
This theorem is referenced by:  elid  6062  cocnvcnv2  6122  f1ovi  6699  ttrclco  33517
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