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Theorem dfrel3 6186
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 6177 . 2 (Rel 𝑅𝑅 = 𝑅)
2 cnvcnv2 6181 . . 3 𝑅 = (𝑅 ↾ V)
32eqeq1i 2736 . 2 (𝑅 = 𝑅 ↔ (𝑅 ↾ V) = 𝑅)
41, 3bitri 274 1 (Rel 𝑅 ↔ (𝑅 ↾ V) = 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1541  Vcvv 3473  ccnv 5668  cres 5671  Rel wrel 5674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702  ax-sep 5292  ax-nul 5299  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4523  df-sn 4623  df-pr 4625  df-op 4629  df-br 5142  df-opab 5204  df-xp 5675  df-rel 5676  df-cnv 5677  df-res 5681
This theorem is referenced by:  elid  6187  cocnvcnv2  6246  f1ovi  6859  ttrclco  9695
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