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Theorem ex-br 26680
 Description: Example for df-br 4584. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-br (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 3𝑅9)

Proof of Theorem ex-br
StepHypRef Expression
1 opex 4859 . . . 4 ⟨3, 9⟩ ∈ V
21prid2 4242 . . 3 ⟨3, 9⟩ ∈ {⟨2, 6⟩, ⟨3, 9⟩}
3 id 22 . . 3 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 𝑅 = {⟨2, 6⟩, ⟨3, 9⟩})
42, 3syl5eleqr 2695 . 2 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → ⟨3, 9⟩ ∈ 𝑅)
5 df-br 4584 . 2 (3𝑅9 ↔ ⟨3, 9⟩ ∈ 𝑅)
64, 5sylibr 223 1 (𝑅 = {⟨2, 6⟩, ⟨3, 9⟩} → 3𝑅9)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∈ wcel 1977  {cpr 4127  ⟨cop 4131   class class class wbr 4583  2c2 10947  3c3 10948  6c6 10951  9c9 10954 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584 This theorem is referenced by: (None)
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