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Theorem dfrel3 6188
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 6179 . 2 (Rel 𝑅𝑅 = 𝑅)
2 cnvcnv2 6183 . . 3 𝑅 = (𝑅 ↾ V)
32eqeq1i 2729 . 2 (𝑅 = 𝑅 ↔ (𝑅 ↾ V) = 𝑅)
41, 3bitri 275 1 (Rel 𝑅 ↔ (𝑅 ↾ V) = 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1533  Vcvv 3466  ccnv 5666  cres 5669  Rel wrel 5672
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-br 5140  df-opab 5202  df-xp 5673  df-rel 5674  df-cnv 5675  df-res 5679
This theorem is referenced by:  elid  6189  cocnvcnv2  6248  f1ovi  6863  ttrclco  9710
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